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Simplfications

Simplifications are very important in Bank Exams. In Quantitative Aptitude /Numerical Ability section, about 40 − 50% of questions in clerical exam and about 20 − 25% of questions in Probationary Officers exam will be of simplifications. 

All simplification questions are to be solved based on BODMAS rule only.
      B − Bracket
      O − Of
      D − Division
      M − Multiplication
      A − Addition
      S − Subtraction
     When there are more brackets in the given expression, simplification should be started from inner most bracket to the outer most bracket.
Some Important Identities 

* (a + b)2 = a2 + b2 + 2ab
* (a − b)2 = a2 + b2 − 2ab

* (a + b) (a − b) = a2 − b2
*(a + b)3 = a3 + b3 + 3a2 b + 3ab2
* (a − b)3 = a3 − b3 − 3a2 b + 3ab2
* a3 + b3 = (a + b) (a2 − ab + b2)
* a3 − b3 = (a − b) (a2 + ab + b2)
* (a + b + c)2 = a2 + b+ c2 + 2ab + 2bc + 2ac
* a3 + b3 + c3 − 3abc = (a + b + c) (a2 + b2 + c2 − ab − bc − ac)
Laws of Indices 

Squares and Cubes of numbers are very useful in simplification questions. Following table gives squares and cubes of 25 numbers

AVERAGES


Examples

Example 1. A batsman has a certain average runs for 16 innings. In the 17th inning he made a score of 85 runs thereby his average is increased by 3. What is his average after 17th inning?
Sol: The average for 17th inning has been increased by 3.
 The total increase in the runs for 17th inning = 17 × 3 
                                     = 51
 But the batsman scores 85.
 Average runs in his 16th innings = 85 -51 
                            = 34.
 Hence the average of runs after 17th innings = 34  + 3 
                                                = 37
Example 2.  A man has 7 children. When their average age was 12 years, the child who was 6 years of age, died. What was the average age of surviving children 5 years after the death of the above child?
Sol: Average age of 7 children  = 12 years
Total age of 6 children  =  12 × 7 = 84 years
Total age of 6 children after the death of a child aged 6 years = 84- 6 = 78
Hence   the average age of the surviving children = 
After 5 yrs. = 13 + 5 = 18 yrs.
Example 3.  If the weights of 5 students of a class are 49.6 kg, 39.8 kg, 45.2 kg and 24.6 kg respectively then what is their average weight?
Sol: Total weight of 5 students = 49.6 + 39.8 + 40.8 + 45.2 + 24.6
                      = 200 kg.
Their average weight =  
                    = 40 kg.
Example 4.  The average temperature for Monday, Tuesday and Wednesday was 36ºC  . The average temperature for Tuesday, Wednesday and Thursday was. If the temperature for Thursday was 37ºC, what was the temperature on Monday?
Sol:   Average temperature for Monday, Tuesday and Wednesday = 36ºC
Total temperature for Monday, Tuesday and Wednesday = 36 × 3 
                                          = 108ºC
Average temperature for Tuesday, Wednesday and Thursday = 38ºC
Total temperature for Tuesday, Wednesday and Thursday = 38 × 3 
                                           = 114ºC  
Total temperature for Tuesday and Wednesday only = 114 - 37 
                                     =  77ºC
Temperature for  Monday only = 108 – 77 
                         = 31ºC
Example 5.  A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.

Example 6.  A vehicle travels from A to B at the speed of 40 km/hr, but from B to A at the speed of 60km/hr. what is its average speed during the whole journey?
Sol: Let the distance from A to B be x km


Example 7.  The average age of a class of 40 boys is 16.95 years. A new boy joins the class and the average age now is 17 years. What is the age of the new boy?
Sol:  The average age of 40 boys  = 16.95 years
                Total are of 40 boys  = 16.95 × 40
                                 = 678 years
        The average age of 41 boys  = 17 years
                Total age of 41 boys  = 17 × 41
                                = 697 years
                 Age of the new boy  = 697 – 678
                                = 19 years

(Writer - G.S.Giridhar)

PERCENTAGES

         A fraction with denominator 100 is called percentage. Numerator of that fraction is called rate percent.
The term percent means per every 100.
50 percent means 50 out of 100.
The symbol  % is used to denote percent. Ex: 20%, 35%, 80% etc.
Percent to fraction: To convert percent into fraction, divide the percent by 100.

Fraction to percent: To convert fraction into percent, multiply the fraction by 100.

Increment percent = 
Ex: increment % in 5 and 8  is  3/5  × 100 = 60%.
Decrement percent  =  
Ex. Decrement % in 5 and 8 is 5/8  × 100 = 37.5%. 
Some important percent /fractions.

             Following rules should be kept in mind for solving the questions on percentage
1. For converting a given percentage into a fraction, divided it by 100 or multiply by 
2. For converting a given fraction into a percentage multiply it by 100.
3. For converting one given quantity, say, x as a percentage of another given quantity, say, y find 
   Note - percentage is never expressed in any unit like rupees or kilos.
4. When there are two articles ‘a’ and ‘b’ in a group and in the ratio of a : b then to express any one article as a percentage of the group, divide the article by the total articles of the group and multiplies the whole by 100.
Percentage of ‘a’ = 
And, Percentage of ‘b’ = 

EXAMPLES

Example 4. How many percent is 15 cm of 1 metre?

Note: Both quantities are converted into same unit.
Example 5.  A person spent 85% of his monthly income and thereafter saves Rs.360 per month. Find out his total income.
Sol: Suppose his monthly income is Rs. 100
Expenditure = 85% = Rs. 85
Saving = Rs. 100 – 85 = Rs. 15
If saving is Rs. 15 income is Rs. 100
If saving is Rs. 360 income is  
                                                 = Rs. 2400
Example 6. If a student gets 38 marks out of 50, what is the percentage of his obtained marks?
Sol:  Percentage of obtained marks  
                                                                = 76%
Example 7.  If two numbers are respectively 30% and 40% more then a third number, what percentage is the first of the second?
Sol: Let the third number be 100
          First number  = 100 + 30% of 100
                                = 130
 and Second number   = 100 + 40% of 100
                                = 140
  Percentage of the first number to the second number to the second number 

Example 8. A student scores 20% marks and fails by 30 marks while another student who scores 32% marks, gets 42 marks more than the minimum required pass marks. What are the maximum marks for the examination?
Sol:   32% - 20% = 12%
      And 42–(-30) = 72
       12% marks = 72          
    100% marks = 
Example 9.  An engineering student has to secure 50% marks to pas. He gets 163 marks and fails by 37 marks. Find the maximum marks
Sol: Minimum marks required = 163 + 37  = 200
         If 50 are the minimum marks then maximum marks  = 100
    200 are the minimum marks then maximum marks =                                                                                                                
 

ఇవి చేయకండి

బ్యాంకు పరీక్షలో విజయం సాధించాలంటే అభ్యర్థులకు ఏమి చేయాలన్నదానితో పాటు ఏమేం చేయకూడదో కూడా తెలియటం తప్పనిసరి. అవేమిటో చూద్దాం. 
‣ ప్రిపరేషన్‌ ఎక్కడ, ఎలా మొదలు పెట్టాలో తెలియకపోవడం
‣ టైమ్‌టేబుల్‌ అనుసరించకపోవడం
‣ తాము నిర్దేశించుకున్న పరీక్షా ప్రణాళికను వదిలివేయడం
‣ కేవలం రోజులో ఎన్ని గంటలు చదివామో అని మాత్రమే గమనించుకోవడం
‣ కొన్ని విభాగాలను అశ్రద్ధ చేయడం
‣ అన్ని కాన్సెప్టులపై పట్టులేకపోవడం
‣ తాము బాగా చేయగలిగే టాపిక్స్‌పై నిర్లక్ష్యం వహించడం
‣ మోడల్‌ పేపర్లు/ ప్రీవియస్‌ పేపర్లు సాధించకపోవడం
‣ రాసిన మోడల్‌ పేపర్‌ను విశ్లేషించుకోకపోవడం
‣ పరీక్షా విధానంలోని ఆన్‌లైన్‌ టెస్టులను సాధన చేయకపోవడం
‣ టాపిక్స్‌ను రెగ్యులర్‌గా పునశ్చరణ (రివిజన్‌) చేయకపోవడం
‣ పరీక్ష రాయటంలో తమ వేగం, కచ్చితత్వం గమనించుకోకపోవడం, వాటిని మెరుగుపరుచుకోకపోవడం
‣ ప్రతిరోజూ వార్తాపత్రికలు చదవకపోవడం. కరెంట్‌ అఫైర్స్‌, ఫైనాన్షియల్‌/బ్యాంకింగ్‌ వార్తలను పట్టించుకోకపోవడం
‣ దృష్టినంతా ప్రిలిమ్స్‌ పరీక్ష పైన మాత్రమే పెట్టడం
‣ సోషల్‌మీడియాను వదల్లేక దానిలో విలువైన సమయం వృథా చేయడం
‣ లక్ష్యసాధనకు అవసరమైన ప్రేరణను పరీక్ష రాసేవరకూ కొనసాగించకపోవడం
వీటన్నింటినీ అనుకూలంగా మార్చుకుంటే ఫలితం తప్పక వస్తుంది. అభ్యర్థులూ.. గుర్తుంచుకోండి- విజయం సాధించాలంటే మీరు మాత్రమే కష్టపడాలి. వేరెవరో మీకోసం ఏమీ చేయలేరు!

Profit & Loss

The money spent to purchase an article is cost price of the article, and the money received for selling an article is called selling price.
                               Profit = selling price – cost price
                                Loss = cost price – selling price

Profit or loss percent is always calculated on C.P unless it is required to calculate on S.P.

DISCOUNTS
        The price at which the article is marked is the marked price or listed price or labeled price or catalogue price.
        The discount is allowed on marked price for the cash payments.
                    
       When discount is deducted from the marked price, the remainder becomes the selling price.
       To find Marked price from Cost Price we can use the following formula
                   
EXAMPLES

Example 1.   Ram sold a cow for Rs.136 at a loss of 15%. At what price should he have sold it to gain 15%?
Sol: Let the cost price be Rs.100 then for 15% loss the S.P = 85 and for 15% profit it should  be Rs. 115.
         Rs. 85 is the first S.P, then second S.P. = Rs. 115
         Rs. 136 is the first S.P =  
Example 2.   A sells a radio to B at a gain of 10% and B sells it to C at a gain of 5%.If C pays Rs. 462 for it, What did it cost to A?
Sol: Let the cost price of A be Rs. 100
        Then the cost price of B be Rs. 110 
         
         
Example 3. A dealer allows 10% discount on the list price of a certain article and yet makes a profit of Rs. 25% on each article. Find the cost price of the article when list price is Rs. 50.
Sol:  Let the cost price of articles be Rs. 100
          Then for 25% profit, S.P.  = Rs. 125
          If list price is Rs. 100, S.P.  = Rs. 90
          If S.P. is Rs. 90, list price  = Rs. 100
          
       Example 4. A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. Had he sold all of them at a uniform profit of 15% he would have got Rs.40 less. Find the cost price of each clock.
Sol: Let the C.P of clock is Rs. 100 each.
        By the profit of 10% S.P. of 40 clocks =  = Rs. 4, 400
        By the profit of 20% S.P of 50 clocks =   = Rs. 6, 000
        Total S.P. = Rs. 4400 + Rs. 6, 000 = Rs. 10, 400
        C.P of 90 clocks =   = Rs. 9000
        By the profit of 15% S.P. of 90 clocks =   = Rs. 10, 350
        Difference = Rs. 10, 400 – Rs. 10, 350 = Rs. 50
        If the difference is Rs. 50 then C.P. = Rs. 100
        If the difference is Rs. 40 then C.P. =  = Rs. 80

Example 5.  A man buys 5 horses and 10 cows for Rs. 1,600. He sells horses at a profit of 15% and cows at a Loss of 10% if his over all profit was Rs. 90, what was the cost price of a horse and a cow?
Sol:  Let x be the cost price of a horse and y be the cost price of a cow
          C.P. of 5 horses = Rs. 5x and C.P of 10 cows = Rs. 10y
        Hence     5x + 10y = 1,600……..(i)
        Since the profit is 15% on the horses  
        
            

NUMBER SYSTEM

    A golden opportunity for Bank exams aspirants. Thousands of posts in SBI and other Banks. Out of five papers in the SBI clerk exam, Quantitative Aptitude plays major role. Arithmetic and Data Interpretation questions will be there in this paper. Arithmetic is the maths, which we use in our day-to-day life. As arithmetic chapters are there upto 10th class only all the aspirants inclusive of non-maths might have studied this. By understanding all the chapters thoroughly and with a lot of practice it is not difficult to solve all the questions of the paper. Also important is simplifications. Out of 40 questions in Q.A., 20 are simplification questions. Students need to mug up tables upto 20, squares of numbers upto 25 and cubes of numbers upto 15 to make simplifications easy. They also learn Speed Maths for solving simplification questions in seconds without pen. All the chapters in arithmetic have to be practiced thoroughly. Let us see all the chapters of arithmetic in detail.
Digit: 0 to 9 are the digits.
Number: By using digits we write numbers.
Face Value: The real value of the digit.
Place Value: The value of the digit according to the place.
e.g.: In 2794, the face value of 7 is '7'and the place value is '700'.
Classification of Numbers:
Odd Numbers
Numbers which are not divisible by 2
e.g.: 1, 3, 5, 7, .......


Even Numbers
Numbers which are divisible by 2
e.g.: 2, 4, 6, 8, .......


Natural Numbers
All counting numbers             e.g.: N = {1, 2, 3, ........}

Whole Numbers
0 and all natural numbers
e.g.: W = { 0, 1, 2, 3, ...}


Integers
Natural numbers, zero and negative of natural numbers
e.g.: I = { ........, -3, -2, -1, 0, +1, +2, +3, .......}


Rational Numbers
These are of the form of p/q, where q π 0
e.g.:  etc


Irrational Numbers
Can't be written in p/q form, where q ≠ 0
e.g.:  π  etc


Composite Numbers
Numbers having more than two factors


Prime Numbers
Numbers divisible by one and the number itself or numbers having only two factors.
e.g.: 2, 3, 5, 7, 11, 13, ...... etc


Some points about prime numbers
All prime numbers end with 1, 3, 7 or 9 except 2 and 5.
* 2 is the only even prime number.
* '1' is neither a prime nor composite number. It is a unitary.
* There are 25 prime numbers upto 100.


Twin prime numbers
The difference between two prime numbers is '2'.
e.g.: 3 - 5, 5 - 7, 11 - 13 etc


Co prime numbers
Numbers not having any common factors.
e.g.: 3, 5 and 8 are co primes to each other.


Some important Identities:
1. (a+b)2 = a2 + b2 + 2ab
2. (a-b)2 = a2 + b2 - 2ab
3. (a+b)(a-b) = a2 - b2
4. (a+b)3 = a3 + b3 + 3a2b + 3ab2
5. (a-b)3 = a3 - b3 - 3a2b + 3ab2
6. a3 + b3 = (a+b)(a2− ab + b2)
7. a3 - b3 = (a− b) (a2 + ab+ b2)
8. (a+b+c)2 = a2+b2+c2 + 2ab + 2bc+2ac
9. a3+b3+c3− 3abc = (a+b+c) (a2 +b2 + c2 - ab -bc-ac)
 
1) 2.01      2) 2       3) 1       4) 1.93        5) None of these
Sol: It is based on the formula a3 + b3 = (a+b)(a2−ab+b2)
1.07 + 0.93 = 2, hence answer (2).
To solve the equations based on numbers, the number is written in algebraic form. 
For example let the number be x.
    The numerator of a fraction is written in the following form
Three-fourth of a number = 
Two-third of a number = 
Double of a number = 2x, Thrice of a number = 3x
20% of a number = 
30% of 3/4 of one-third of a number =  
e.g.: 1.  4/5  of  4/7  of  5/6  of  1218 = ?     (SBI 2008)
(A) 415      (B) 384       (C) 492       (D) 346      (E) None of these
sol:  hence answer (E)
2. One-seventh of a number is 51. What will be 64% of that number?       (SBI 2008)
    (A) 248.12     (B) 228.48      (C) 238.24      (D) 198.36     (E) None of these
Sol:
 

 hence answer (E)

3. If (16)3 is subtracted from the square of a number, the answer so obtained is 3825. What is the number ?      (SBI 2008)
(A) 69     (B) 59     (C) 89      (D) 79    (E) None of these
Sol: Let the number be x  
x2− 163= 3825  x = 89
 hence answer (C).
4. If (92)2 is added to the square of a number, the answer so obtained is 10768. What is the number?          (SBI 2008)
(A) 46         (B) 2304        (C) 48        (D) 2116       (E) None of these
Sol: Let the number be x
x2+ 922= 3825  x = 48
hence answer (C).
5. If an amount of Rs. 97,836 is distributed equally amongst 31 children. How much amount would each child get?    (SBI 2008)
(A) Rs.3,756    (B) Rs.3,556    (C) Rs. 3,356    (D) Rs. 3,156    (E) None of these 
Sol:     hence answer (D).
     Three consecutive odd numbers are x, (x+2) and (x+4), or (x-2), x and (x+2), where x is an odd number.
     Similarly, three consecutive even numbers are x, (x+2) and (x+4) or (x-2), x and (x+2) where x is an even number
     If a number 'a' is multiplied by itself for n times, the product is called n th power of
'a'. This is written as an.
     In an, a is called base and n is called index or exponent or power.
All simplification questions have to be solved based on BODMAS rule only.
  B - Bracket
  O - Of
  D - Division
  M - Multiplication
  A - Addition
  S - Subtraction
e.g. 1: What is 394 times 113? (SBI 2008)
(A) 44402       (B) 44632       (C) 44802      (D) 44522     (E) None of these
Sol:   394 × 113 = 44522,     hence answer (D)
2. What approximate value should come in place of the question mark (?) in the following question?  4780 ÷ 296 × (23)2 = ?
(A) 9870      (B) 6760      (C)7590     (D) 3430      (E) 8540
Sol: × 529 = 8542.63
Approximately 8540, hence answer(E)
3. When 40% of first number is added to the second number the second number becomes 1.2 times of itself. What is the ratio between the first and second numbers?
(A) 2:3      (B) 4:3       (C) 1:2      (D) 5:7      (E) None of these
Sol: Let the first and second number be x and y

RATIO AND PROPORTION

RATIO: Ratio means Comparison. The number of times one quantity contains another quantity of the same kind.
            Thus the ratio between 5 litres of oil and 15 litres of oil can be possible, but not between 10 apples and 25 kg of rice. 
* The ratio between one quantity to another is measured by  a : b or a/b
Ex: 8 : 9   or   5 : 7 etc.
* The two quantities in the ratio are called its terms. The first is called the antecedent and the second term is called consequent.
* The terms of the ratio can be multiplied or divided by the same number.
Types of Ratios:
1. Duplicate ratio: The ratio of the squares of the two numbers.
     Ex: 9 : 16 is the duplicate ratio of 3 : 4.
2. Triplicate Ratio: The ratio of the cubes of the two numbers.
     Ex: 27 : 64 is the triplicate ratio of 3 : 4.
3. Sub-duplicate Ratio: The ratio between the square roots of the two numbers.
      Ex: 4 : 5 is the sub-duplicate ratio of 16 : 25.
4. Sub-triplicate Ratio: The ratio between the cube roots of the two numbers.
      Ex: 4 : 5 is the sub-triplicate ratio of 64 : 125.
5.Inverse ratio: If the two terms in the ratio interchange their places, then the new ratio is inverse ratio of the first.
      Ex: 9 :5 is the inverse ratio of 5 : 9.
6. Compound ratio: The ratio of the product of the first terms to that of the second terms of two or more ratios.
      Ex: The compound ratio of   
PROPORTION: If two ratios are equal, then they make a proportion.
            Thus  
Each term of the ratios   is called proportional.
The middle terms 5 and 8 are called means and the end terms 4 and 10 are called extrems.d
Product of Means = Product of Extremes


Continued Proportion: In the proportion    8, 12, 18 are in the continued proportion.
Fourth proportion: If a : b = c : x, then x is called fourth proportion of a,b and  c.
There fore fourth proportion of  a, b, c  = 
Third proportion: If a : b = b : x, then x is called third proportion of a and b.
Therefore third proportion of a, b =  
Second or mean proportion: If a : x = x : b , then x is called second or mean proportion of a and b.
Therefore mean proportion of a and b =  
1. a : b = 3: 4; b : c = 6 : 7. Find a : b : c.
Sol:    a     b      c
          3     4
                 6      7
a : b : c = 3 × 6 : 6 × 4 : 4 × 7 = 9 : 12 : 14
2. A sum of Rs.4960 has been divided among A, B and C in the ratio of 5:4:7. Find the share of B.
Sol: B's share =  
                          = Rs.1240


3. 36% of first number is 28% of the second number. What is the respective ratio of the first number to the second number?
Sol:  Let the numbers be x and y.
       36% of x = 28% of y
       
          x : y = 7 : 9


4. Two numbers are in 4:7 ratio. The difference between them is 27. What is the bigger number?
Sol:  Let the numbers be 4x and 7x.
             7x - 4x = 27
            3x = 27    x = 9
 Bigger number is 7x = 7 × 9 = 63
Short cut: The difference of the terms of the ratio = 7 − 4 = 3.
 But the actual difference between the numbers is 27 
 3 parts is equal to 27
 7 parts (Bigger number) =  × 27 = 63
5. The ratio of the ages of a man and his son is 7: 3. The average of their ages is 30 years. What will be the ratio of their ages after 4 years?
Sol: Average age = 30 years
Total age = 2 × 30 = 60 years.
Let their present ages be 7x and 3x years
 7x + 3x = 60  x =  = 6
 Their present ages are
7 × 6 and 3 × 6 = 42 and 18.
 Their ages after 4 years
= 42 + 4 and 18 + 4 = 46 and 22 years
 ratio = 46 : 22 = 23 : 11


6. Two numbers are in the ratio of 3:4. If 4 is subtracted from each, the remainders are in the ratio of 5:7. What are the numbers?
Sol: Let the numbers be 3x and 4x.
If 4 is subtracted from each, the numbers will be (3x -4) and (4x -4).
(3x-4) : (4x -4) = 5: 7
Product of means = Product of extremes
(3x-4) 7 = (4x - 4) 5
 21x - 28 = 20x - 20
 x = 8
 The numbers are 3 × 8 and 4 × 8 
                   = 24 and 32


7. In a bowl there is 30 litre mixture of milk and water. The ratio of milk and water is 7:3. How much water must be added to it so that the ratio of milk to the water be 3:7?
Sol : Milk quantity in the mixture
=  ×30 = 21 litres
 Water = 30 - 21 = 9 litres
New ratio = 3 : 7
 3 parts of milk is 21 litres (There is no difference in the milk quantity of new mixture)
 Water quantity in the mixture
=  × 21 = 49 litres
 49 - 9 = 40 litres  water is to be added in the new mixture


8. A bag contains of one rupee, 50 paise and 25 paise coins. if these coins are in the ratio of 5 : 6 : 8, and the total amount of coins is Rs. 210, find the number of 50 paise coins in the bag.
Sol : Let the number of one rupee, 50 paise, 25 paise coins be 5, 6 and 8 respectively
The value of one rupee coins
             = Rs. 1 × 5 = Rs. 5
The value of fifty  paise coins
             = Rs. 0.50 × 6 = Rs. 3
The value of twenty five paise coins
             = Rs. 0.25 × 8 = Rs. 2
Total value = 5 + 3 + 2 = Rs. 10
If the total value is Rs. 10
there are 6 coins of fifty paise
if the total value is Rs. 210, then the number of 50 coins =  × 6 = 126
9. If a sum of Rs.3150 were distributed among Ravi, Vijay and Suresh in the ratio of 12:9:14 respectively, then find the share of Vijay.
Ans: Rs.810
Sol: Vijay's Share =  × 3150 = Rs.810


10. The total number of students in a school is 2850. If the number of boys in the school is 1650, then what is the respective ratio of the total number of boys to the total number of girls in the school?
Ans: 11:8
Sol: Total number of students = 2850
Number of boys = 1650
Number of girls = 2850-1650 = 1200
Ratio between boys and girls
=1650 : 1200 = 11 : 8


11. A sum of money is divided among A, B, C and D in the ratio of 5 : 6 : 12 : 15 respectively. If the share of C is Rs. 4092, then what is the total amount of money?
Ans: Rs. 12958
Sol: Let the share of A, B, C and D be Rs. 5x, 6x, 12x and 15x respectively. C's share is Rs.4092
 12x = 4092   x=  = 341
  Total money = 38x = 38 × 341= Rs.12958


12. Asum of Rs. 2820 has been distributed among A, B and C in the ratio  respectively. What is the share of B?
Ans: Rs. 900
Sol: LCM of 3, 4 and 5 is 60
 ratio =  : 20 : 15 : 12
 B's share =  × 2820
 =   ×2820 = Rs. 900 

13. A, B and C divide an amount of Rs. 6300 amongst themselves in the ratio of 7:6:8 respectively. If an amount of Rs.300 is added to each of their shares, what will be the new respective ratio of their shares of amount?
Ans: 8 : 7 : 9
Sol: Total shares = 7 + 6 + 8 = 21
         21 parts = 6300
       each part =  = 300
 Their shares are
7 × 300, 6 × 300 and 8 × 300
  2100, 1800 and 2400
If 300 is added to each of them then their shares are 2400, 2100 and 2700
Their ratio = 2400 : 2100 : 2700                   
 = 8 : 7 : 9
14.  Find out the two quantities whose difference is 30 and the ratio between them is 5/11.
Sol: The difference of quantities, which are in the ratio 5:11, is 6. To make the difference 30, we should Multiply them by 5.
        Therefore  
15. A factory employs skilled workers, unskilled workers and clerks in the ratio 8:5:1 and the wages of a skilled worker, an unskilled worker and a clerk are in the ratio 5:2:3 when 20 unskilled workers are employed the total daily wages fall amount to Rs. 318. Find out the daily wages paid to each category of employees.
Sol: Number of skilled worker: unskilled worker: clerks = 8:5:1 and the ratio of their respective Wages = 5:2:3
      
Hence the amount will be paid in the ratio 8 × 5 : 5 × 2 : 3 × 1 = 40 : 10 : 3             
Hence total amount distributed among unskilled workers 

But the number of unskilled workers is 20, so the daily wages of unskilled worker 

The wages of a skilled worker, an unskilled worker and a clerk are in the ratio = 5:2:3
Multiplying the ratio by   we get = 7.50 : 3 : 4.50
So, if an unskilled worker gets Rs.3 a day then a skilled worker gets Rs. 7.50 per day a clerks Rs. 4.50 a day

Simple Interest

1. Introduction
» Money is not free and it costs to borrow the money. Normally, the borrower has to pay an extra amount in addition to the amount he had borrowed. i.e, To repay the loan, the borrower has to pay the sum borrowed and the interest.
2. Lender and Borrower
» The person giving the money is called the lender and the person taking the money is the borrower.
3. Principal (sum)
» Principal (or the sum) is the money borrowed or lent out for a certain period. It is denoted by P.
4. Interest
» Interest is the extra money paid by the borrower to the owner (lender) as a form of compensation for the use of the money borrowed.
5. Simple Interest (SI)
» If the interest on a sum borrowed for certain period is calculated uniformly, it is called simple interest(SI).

 6. Amount (A)
The total of the sum borrowed and the interest is called the amount and is denoted by A
7. The statement "rate of interest 10% per annum" means that the interest for one year on a sum of Rs.100 is Rs.10. If not stated explicitly, rate of interest is assumed to be for one year.
8. Let Principal = P, Rate = R% per annum and Time = T years. Then
                            
9. From the above formula , we can derive the followings


                                                     

WHO UNVEILED THE STATUE OF PEACE..?

International

Biden new team
On 24 November 2020, the USA President-elect Joe Biden announced his nominees for key foreign policy and national security roles as the transition process officially began. Antony Blinken will be secretary of state and John Kerry as Climate change envoy. He picked Linda Thomas-Greenfield to represent his nation in UNO as ambassador. He announced many firsts on the team, including Avril Haines, a former deputy director of the C.I.A, who would be the first woman to serve as director of national intelligence, and Alejandro Mayorkas, who would be the first Latino and first immigrant to lead the Department of Homeland Security.
While unveiling the new team Biden said “America is back” and noted that Jake Sullivan, his choice to serve as National Security Adviser, would be the youngest person to coordinate the national security team in decades.


12th BRICS Summit
On 17 November 2020, Prime Minister Narendra Modi virtually participated in the 12th summit of BRICS (Brazil Russia - India - China - South Africa) group. This year's theme was 'Global stability, shared security and innovative growth'. While addressing the meet, PM Modi reiterated India's long-standing demand for reformed multilateralism. He also touched upon the need to reform the United Nations Security Council (UNSC) in light of contemporary challenges. Russian President Vladimir Putin announced the approval of the Moscow Declaration, the BRICS Anti-Terrorism Strategy and the BRICS updated strategy for the economic partnership until 2025 at the culmination of the 12th BRICS summit.


India’s own IRNSS
On 11 November  2020, India became the fourth country in the world to have its independent regional navigation satellite system recognised by the International Maritime Organisation (IMO) as a part of the World Wide Radio Navigation System (WWRNS). Now this navigation system can replace GPS (Global Positioning Systems) in the Indian Ocean waters up to 1500 km from the Indian boundary.  By this, India has become the fourth country to have its independent regional navigation system after the USA, Russia and China.


'My understanding about Gandhi'
A special anthology on Mahatma Gandhi 'Maile Bujheko Gandhi' (My understanding about Gandhi) was released by Nepal President Bidhya Devi Bhandari during a ceremony at Kathmandu on 9 November 2020. The pictorial anthology in Nepalese has been released to celebrate 151st Birth Anniversary of Mahatma Gandhi and to mark the culmination of the two years long celebrations of '150 years of Mahatma'. The book has been brought out by the Embassy of India along with the BP Koirala India-Nepal Foundation. 


Second World Health Expo
The Second World Health Expo was held between 11-14 November 2020 in Wuhan, the capital city of Central China’s Hubei Province.  The expo features 12 different venues for audiences to experience the most frontier health technology. 

 

APEC 2020
Asia-Pacific Economic Cooperation (APEC) began on 20 November 2020 hosted by Malaysia. The official theme of the summit is "Optimising Human Potential Towards a Resilient Future of Shared Prosperity: Pivot. Prioritise. Progress". After the virtual summit, the leaders issued the Kuala Lumpur Declaration. They adopted the Putrajaya Vision 2040, which is a new 20-year growth vision to replace the Bogor Goals named after the Indonesian town where leaders agreed in 1994 to free and open trade and investment. The leaders also pledged to build an “open dynamic, resilient and peaceful region” by 2040. 


UMANG International Version
On 23 November 2020, UMANG app's international version was launched by Union IT Minister Ravi Shankar Prasad
during a virtual conference to mark three years of the platform. The UMANG (Unified Mobile Application for New-age Governance) app provides a single platform to access pan India e-governance services ranging from central to local government bodies, and other citizen-centric services. It will help Indian international students, NRIs and Indian tourists abroad, to avail Government of India services, anytime.


G 20 Summit
Prime Minister Narendra Modi stressed the importance of reforms in multilateral organisations to ensure better global governance for faster post-Covid recovery at the G-20 Summit hosted by Saudi Arabia between 21-22 November 2020. The theme of the summit was "Realising the Opportunities of the 21st Century for All”. The G-20 Riyadh Summit Leaders Declaration said that G 20 next meetings will be in Italy in 2021, Indonesia in 2022, India in 2023 and Brazil in 2024.

 

National

Varunastra
The Chairman of DRDO, G.Satheesh Reddy, flagged off the first Varunastra, the Heavy Weight Torpedo, being delivered to the Indian Navy, at a ceremony held at Bharat Dynamics Limited (BDL) Visakhapatnam Unit on 21 November 2020. Varunastra  has been designed and developed by NSTL (Naval Science & Technological Laboratory) Visakhapatnam. Varunastra is a ship-launched, heavyweight, electrically-propelled anti-submarine torpedo capable of targeting quiet submarines, both in deep and shallow waters in an intense countermeasures environment.


Safaimitra Suraksha Challenge
On 19 November 2020, the Union minister of state Housing and Urban Affairs (Independent Charge) Hardeep Singh Puri launched the Safaimitra Suraksha Challenge, to ensure that no person needs to enter a sewer or septic tank, unless unavoidable in the interest of greater public hygiene. The virtual event witnessed participation of representatives from 243 cities across the country, coming together to take a pledge to mechanize all sewer and septic tank cleaning operations by 30th April 2021. The Challenge will focus extensively on creating citizen awareness on this critical issue along with infrastructure creation for mechanized cleaning and capacity building of the workforce. The initiative was launched on the occasion of World Toilet Day, observed every year on 19 November.


Lilavati Awards 2020
On 17 November 2020, Union Education Minister Ramesh Pokhriyal ‘Nishank’ launched AICTE’s Lilavati Awards 2020 virtually. The Theme of the award is “Women Empowerment”. This award intends to recognize the efforts being made by AICTE approved institutions to treat women with ‘equality and fairness’ in all spheres of their lives.

 

Statue of Peace 
Prime Minister Modi unveiled the 151inch tall “Statue of Peace” to mark 151st Birth Anniversary of Jainacharya Shree Vijay Vallabh Surishwer Ji Maharaj on 16 November 2020 which was installed at Vijay Vallabh Sadhana Kendra, Jetpura, in Pali, Rajasthan. Shree Vijay Vallabh Surishwer Ji Maharaj (1870-1954) led an austere life as a Jain Saint working selflessly and dedicatedly to spread the message of Lord Mahavira.


SITMEX-20
The Second edition of India, Singapore and Thailand Trilateral Maritime Exercise SITMEX-20 was held from 21 to 22 November 2020 in the Andaman Sea. The exercise was conducted to increase the mutual inter-operability and imbibing best practices among the three naval forces. This year SITMEX hosted by Singapore.

 

Vaccine review tour
On 28 November 2020, Prime Minister Narendra Modi visited three cities to review the vaccine development and manufacturing process for COVID being done by various pharma companies. He visited the Zydus Biotech Park in Ahmedabad, Bharat Biotech in Hyderabad and Serum Institute of India in Pune.


All India Presiding Officers Conference
President Ram Nath Kovind inaugurated the 80th All India Presiding Officers Conference at Kevadia, Gujrat on 25 November 2020.  The Theme of the conference was ‘Harmonious Coordination between Legislature, Executive and JudiciaryKey to a Vibrant Democracy’.  The Lok Sabha Speaker and the Chairman of the All India Presiding Officers Conference Om Birla said that there will be a commitment to implement the decisions taken during the two-day conference in a phased manner.  


Garima Greh..  
On 25 November 2020, the Union Minister for Social Justice & Empowerment Thaawarchand Gehlot inaugurated ‘Garima Greh, the Shelter Home for Transgender Persons’ in Vadodara, Gujarat virtually. He also e-launched a ‘National Portal for Transgender Persons’. The Portal would help a transgender person in applying for a Certificate and Identity card digitally from anywhere in the country without having to visit any office. It should be noted that the Transgender Persons (Protection of Rights) Act, 2019 came into effect on 10th January 2020 is the first concrete
step towards ensuring the welfare of Transgender persons.


PRAGTI meeting
Prime Minister Narendra Modi chaired the 33rd PRAGTI (Pro-Active Governance and Timely Implementation) meeting on 25 November 2020.  In this, multiple projects, grievances and programmes were reviewed involving the cost of Rs 1.41 lakh crore that were related to ten states and union territories. 


Bengaluru Tech Summit
On 19 November 2020, Prime Minister Narendra Modi inaugurated the Bengaluru Tech Summit (BTS) 2020 virtually.  PM had given a call to the young talents to create robust cybersecurity solutions to protect our data and IT-based products.  Prime Minister of Australia Scott Morrison participated in the meet who said that Bengaluru is India's biggest tech cluster.

 

Others

2020 UN Population Award
On 11 November 2020, the Queen Mother of Bhutan, her Majesty Gyalyum Sangay Choden Wangchuck, was announced as the individual laureate for the 2020 United Nations Population Award.  HelpAge India was announced as the award’s institutional laureate. Gyalyum Wangchuck is a longstanding champion of sexual and reproductive health and rights and the need to end violence against women, girls and children in Bhutan. The world’s ageing population has
gained increasing attention in recent years, but HelpAge India has been working with and for disadvantaged elderly people in India for nearly four decades. Established by the United Nations General Assembly in 1981, the United Nations Population Award recognizes contributions in the fields of population and reproductive health.


Vatayan Award
Union Education Minister Ramesh Pokhriyal was conferred with the Vatayan Lifetime Achievement Award for his exemplary contribution in the field of literature on 21 November 2020. The award was conferred in an online ceremony for his contribution in the field of literature. The award - given by the VatayanUK organisation in London - honours poets, writers and artists for exemplary work in their respective fields. Nishank earlier received several awards in the field of literature and administration including Sahitya Bharati award, Sahitya Gaurav Samman and Bharat Gaurav Samman.

 

Jallikattu
A Malayalam film about a hunt for a bull on the run ‘Jallikattu’ was selected as this year's Oscar entry in the Best International Feature Film category of the 93rd Academy Awards 2021. The film directed by Lijo Jose Pellissery. The film was premiered at the Toronto Film Festival and was also screened at the Busan festival. It is based on a short story by the writer S Hareesh titled Maoist. 


International Children's Peace Prize
On 14 November 2020, Sadat Rahman, a teenager from Bangladesh won the International Children's Peace Prize for his efforts to educate young people about cyberbullying. He was inspired to create this mobile app to help young people report online abuse after hearing about a 15-year-old girl who took her own life because of bullying. The prize is given away by the international children’s rights organization KidsRights to a child, who fights courageously for children’s rights.


National Newborn Week 2020
National Newborn Week 2020 observed from 15 November to 21 November. The theme of the National Newborn Week is 'Quality, equity, dignity for every newborn at every health facility and everywhere’. On this eve, Union Health Minister
Harsh Vardhan said that India has successfully met the 2017 target of the newborn mortality rate of 24 per 1,000 live births and is making efforts to fulfil the target of stillbirth rate of 19 per 1,000 total births by this year. He released a detailed progress card on India Newborn Action Plan targets. He further added that a newborn mortality rate of 23 per 1,000 live births as per the Sample Registration System (SRS), 2018, and estimates of the United Nations Inter-Agency Group for Child Mortality Estimation (UNIGME).


Booker Prize
Douglas Stuart of Scotland won the Booker Prize for fiction ‘Shuggie Bain’ on 19 November 2020.  The prestigious 50,000 pounds ($ 66,000) award conferred on his debut novel about a boy in Glasgow (Scotland) trying to support his mother, as she struggles with addiction and poverty. Stuart dedicated his book and his prize to his mother, who died of alcoholism when he was 16. Burnt Sugar, a novel written by Avni Doshi, the Indian origin American woman author, settled in Dubai is one among the nominated books for this coveted prize.

 

Model Questions

1. Who was re-elected as the president of Athletics Federation of India?
1) Dr Michael Irani     2) Rohan Jaitley      3) Adille Sumariwalla     4) Anil Jain     5) Gyanendro Ningombam

 

2. The USA President-elect Joe Biden appointed an Indian-American as the policy director of his wife Jill Biden. He/ She is……..
1) Manga Anantatmula      2) Renu Khator     3) Sruthi Palaniappa      4) Rita Baranwal     5) Mala Adiga

 

3. Abhayam, the project for safety and security of women passengers launched by…....
1) AP       2) Telangana       3) Kerala        4) MP        5) Delhi

 

4. India International Cherry Blossom Festival, the calendar event of which state cancelled this year in the wake of COVID-19 pandemic?
1) Manipur      2) Nagaland     3) Mizoram      4) Meghalaya       5) Tripura

 

5. Women's T-20 World Cup 2023 to be hosted by……….
1) India       2) Australia      3) South Africa      4) Sri Lanka      5) New Zealand


6. Delhi got 62nd rank in the list of World’s Best Cities for 2021 prepared by Resonance Consultancy Limited. Which city got the first rank in the world?
1) New York      2) Paris      3) Moscow      4) London      5) Los Angles

 

7. Which nation successfully launched its Chang'e-5 lunar mission to collect rocks from the moon?
1) Japan     2) North Korea     3) China     4) South Korea     5) Thailand

 

8. 14-year-old girl won the prestigious Children's Climate Prize for designing a mobile ironing cart using solar panels to power a steam iron box rather than conventional charcoal. She is........
1) Vinisha Umashankar     2) Aishwarya Sridhar     3) Seema Gupta      4) Sudha Painuli       5) Neelakantha Jonnalagadda

 

9. Who is elected as the new chairman of International Cricket Council (ICC)?
1) Giovanni Infantino      2) Jacques Rogge     3) Greg Barclay      4) Thomas Bach     5) Chris Kermode

 

10. Francisco Sagasti was sworn in as interim president of which nation on 17 November 2020?
1) Peru     2) Moldova     3) Ivory Coast     4) Tanzania     5) Kosovo

 

11. Aung San Suu Kyi's ruling National League for Democracy (NLD) claimed a victory in Myanmar’s second parliamentary election. What is the currency of Myanmar?
1) Kyat       2) Taka       3) Shilling        4) Rupee    5) Tenge

 

12. List of important days given. The correct combination is...
1) National Education Day-11 NOV      2) Public Service Broadcasting Day-12 NOV
3) Samvidhan Diwas or Constitution Day - 26 NOV     4) World Toilet Day - 19 NOV     5) All of above


13. India’s longest single-lane motorable suspension bridge in Tehri Garhwal district on Tehri lake was inaugurated in………
1) Chhattisgarh     2) Assam    3) Arunachal Pradesh    4) Uttarakhand     5) Maharashtra

 

14. Who was appointed as state icon of Punjab by the Election Commission of India?
1) Chacha Chaudhary    2) Harmanpreet Kaur     3) Sonu Sood    4) Yuvraj Singh     5) Harbhajan Singh

 

15. Which Cyclone caused damage in the states of Tamil Nadu, Puducherry and Andhra Pradesh recently?
1) Gaja         2) Gati         3) Nivar       4) Goni         5) Eta

 

16. Who is the author of the book ‘A promised Land’?
1) Shashi Tharoor     2) Boris Johnson     3) Barack Obama     4) Romila Thapar     5) Pope Francis

 

17. The 2021 United Nations Climate Change Conference, also known as COP26 to be hosted between 1-12 November 2021 at……….
1) Zurich, Switzerland     2) Paris, France    3) Bonn, Germany    4) Buenos Aires, Argentina    5) Glasgow, Scotland

 

18. ‘Delhi Crime’  won the best drama series honour at the 48th International Emmy Awards. Who is the director of the series?
1) Ismail Umar Khan     2) Garry Bhinder     3) Sumeet Sachdev     4) Richie Mehta     5) Krishna CH

 

19. World’s first library for children on a tram launched in….
1) Pune    2) Chennai    3) Kolkata      4) Cuttack     5) Aizawl

 

20. Lonar Lake in which state has been chosen as a wetland site of international importance under the Ramsar conservation treaty?
1) Karnataka      2) Maharashtra      3) MP       4) Assam       5) Jammu and Kashmir

 

Key:  1-3;   2-5;  3-1;  4-4;  5-3;  6-4;  7-3;  8-1;  91-3;   10-1;   11-1;   12-5;   13-4;   14-3;  15-3;   16-3;  17-5;   18-4;   19-3;   20-2.

Data Interpretation

          Data Interpretation can be called as comprehension of mathematics. In reading comprehension, we have to study the passage and answer the questions followed by that.
Similarly, in Data Interpretation, data is given in the form of graphs, charts and tables followed by questions. We have to study, understand and analyse the data to solve the questions.

DATA: Data is a collection of facts, such as values or measurements. It can be numbers, words, measurements, observations or even just descriptions of things.
         Information refers to data being arranged and presented in a systematic or an organise form, so that some useful inference can be drawn from the same. By data we generally mean quantities, figures, statistics, relating to any event.

 

What is DATA INTERPRETATION?
         Data Interpretation is the extraction of maximum information from a given set of data or information. The data can be presented either in the form of a table or a bar chart or a pie chart or a line graph or as a combination of one of these formats.

Tips in solving DI questions: The following tips may help in answering problem solving questions that involve data analysis:
¤ Before starting DI section one should be very comfortable with numbers, calculations, fractions, percentages, averages, ratios. It helps in reducing the time required for solving the questions.
¤ Scan the data briefly to see what it is about, but do not attempt to analyse it in too much detail before reading a question. Focus on only those aspects of the data that are necessary to answer the question.
¤ Be sure to read all notes related to the data.
¤ When possible, try to make visual comparisons of the data given in a graph and estimate products and quotients rather than perform involved computations. Remember that these questions are to be answered only on the basis of the data given, everyday facts (such as the number of days in a year), and your knowledge of mathematics.
¤ Do not make use of specific information you recall that might relate to the particular situation on which the questions are based unless that information can be derived from the date provided.
     Let us see some of the graphs of various types.


BAR DIAGRAM: A bar diagram is that two dimensional graphic representation where the elementary graphic objects are a set of rectangles (bars) drawn in parallel so that the extension of the same is proportional to the magnitude they intend to represent.
        The rectangles, or bars, can be either horizontally or vertically positioned.

Simple bar diagram: If only one bar is given in the graph that is called simple bar diagram. E.g.: Following bar diagram gives the production of a company in various years.
                                 

Pb: What is the average production of the company over the years?
       1) 350                  2) 200                   3) 450                   4) 300                  5) None of these
Sol: Average production
    

Multiple Bar diagram: When more than one adjacent vertical bars given then that is called multiple bar diagram.
                             
E.g.: The bar-diagram gives imports and exports of a country over the years.
Pb: The imports in 2000-01 is what percent of the imports in 2002-03?
        1) 25%              2) 100%                 3) 20%              4) 80%              5) None of these

Sol: Imports in 2000 - 01 is 400

       Imports in 2002 - 03 is 500
   

Sub-divided or component bar diagram: Sub-divided or component bar chart is used to represent data in which the total magnitude (bar) is divided into different parts or components. In this diagram, first we make simple bars for each class taking total magnitude in that class and then divide these simple bars into parts in the ratio of various components.
E.g.: Following graph gives the production of vehicles by three companies P, Q and R over the years. Production is in thousands.

Pb: What is the difference between the production of Q in 1997 and 1999?
        1) 1250         2) 2000            3) 2500             4) 2250         5) None of these
Sol: Production of Q in  1997 is (40 -17.5) = 22.5 thousand
         Production of Q in 1999 is (32.5-12.5) = 20 thousand
        Difference = 22500 - 20000 = 2500 Hence answer is (3)

Line Graphs: A line graph is a type of graph, which displays information as a series of data points connected by straight line segments or A graph that uses points connected by lines to show how something changes in value.
                              

E.g.1: The line graph gives the production of a company over the years.
Pb: In how many of the following years was the production of the company above the average?
       1) 2                 2) 4                       3)1                       4) 5                       5) None of these
Sol: Average production 
         ∴ Production is above average in three years.                              hence answer is (5)
E.g.2: Following graph shows the profit (in lakhs) of two companies A and B over the years.
                             

Pb: What is the difference between the average profit of the companies A and B over the years?

       1) 2.5 lakh            2) 5 lakh             3) 4.75 lakh          4) 3.33 lakh           5) None of these
Sol:            Average profit of
           

PIE CHART: A pie chart is a circular chart divided into sectors. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents.
E.g.: Following Pie-chart shows the different colours of cars using by 7200 persons in a town.
Pb: How many persons are using red colour cars?

      1) 720               2) 1440                 3) 1050                 4) 360                   5) None of these
Sol: Number of persons using red colour cars is 
         
        Hence answer (2)

TABLES:
Data is given in rows and columns. A row is a series of cells going horizontally across the table. A column is a series of cells going vertically or up and down the table.
E.g.: Following table gives the number of computers produced by five companies, P, Q, R, S and T over the years. Production is in thousands.

Pb: The percentage lead in the production of computers by company R from 2005 to 2006 was
        1) 20%             2) 30%              3) 25%               4) 50%               5) 32.5%

    Hence answer (4)

Data Interpretation

BAR DIAGRAMS

Directions (Q.1 - 5): Study the following graph carefully and answer the questions accordingly. Following graph shows the requirement and production (in thousand tons) of rubber over   the years.

1. In 2011, the production of rubber was what percent of the requirement (rounded off to   two digits after decimal)?
1) 58.48%       2) 69.23%       3) 144.44%
4) 71.57%       5) None of these


2. What is the average requirement over the  years?
1) 6,300 tons       2) 57,000 tons        3) 5,300 tons
4) 61,000 tons     5) None of these


3. In which of the following years was it likely   that the quantity of rubber imported to bridge   the gap between demand and supply was   minimum?
1) 2012               2) 2009          3) 2011
4) 2013               5) 2010


4. What is the respective ratio between the production of rubber in 2012 and production in 2010?
1) 10 : 13      2) 11 : 15     3) 12 : 13
4) 13 : 10      5) None of these


5. The requirement of rubber in 2011 is approximately how much percent more than the requirement from the previous year?
1) 15%        2) 21%     3) 14%      4) 18%      5) 16%


Directions (Q.6 - 10): Study the following bar diagram carefully to answer the questions that  follow.
Following bar diagram gives the Profit (in Rupees crores) earned by a company over   the years.

6. The expenditure of the company in the year 2009 was Rs.65 crores, what was the income of the company in that year?
1) Rs.5 cr              2) Rs.85 cr               3) Rs.115 cr
4) Rs.135 cr          5) None of these


7. What is the average profit earned by the company over the years approximately?
1) Rs.65 cr         2) Rs.63 cr           3) Rs.61 cr
4) Rs.71 cr         5) Rs.69 cr


8. The income of the company in the year 2011 was Rs.120 crores and the income of the company in the year 2008 was Rs.85 crores. What is the respective ratio of the expenditure  of the company in the year 2011 to the  expenditure of the company in the year  2008?
1) 1 : 2       2) 5 : 9       3) 2 : 3     4) 3 : 7       5) None of these


9. What is the percent profit of the year 2012, if the income of the company was Rs.95  crores?
1) 57.8%          2) 137.5%        3) 80%
4) 55%             5) None of these


10. In which of the following years was the percentage   increase in the profit the highest   from that of the previous year?
1) 2011           2) 2008       3) 2009
4) 2013           5) 2010


Directions (Q.11 - 15): Study the graph carefully  to answer the questions that follow.  Following graph gives the Number of employees   (in hundreds) in different income groups   from three different organizations A, B and C.

11. Which income group has the minimum number  of employees?
1) 14001-17000           2) 20001 - 23000        3) 5001 - 8000     

4) 11001-14000           5) 17001 - 20000


12. What is the respective ratio of number ofemployees from income groups 8001- 11000, 14001-17000 and 20001-23000  together of organization B to those from the  same income groups of organization A?
1) 16 : 17       2) 13 : 14        3) 19 : 20
4) 34 : 35       5) None of these


13. What is the total number of employees in  organisation C in all the income groups   together?
1) 3500             2) 3750            3) 3350
4) 3450             5) None of these


14. Number of employees in the income group  of 14001-17000 from organization B is what  percent of the employees from organization  A in the income group of 11001-14000?
1) 33%          2) 66.66%        3) 75%
4) 125%        5) None of these


15. Number of employees in the income group  of 20001-23000 of organisation B is  approximately how much percent less than   that of the income group 11001-14000 of   the same organization?
1) 25%         2) 35%    3) 40%     4) 30%     5) 20%


Directions (Q.16 - 20): Study the following graph and answer the questions that follow. The following graph shows the ratio of  Imports and Exports of two companies A and B  over the years.

16. In how many of the given years were the  imports more than the exports for company B?
1) 1     2) 5    3) 3   4) 4    5) None of these


17. What were the average exports of company A over the given years?
1) Rs.34 cr     2) Rs.14 cr     3) Rs.28 cr   4) Can’t be determined      5) None of these


18. If the total exports of company B in 2006  and 2008 was 42 crore, then what was the total imports of the same company for these  two years together?
1) 50.4 cr     2) 48.6 cr        3) 47.6 cr       4) Can’t be determined         5) None of these

Key
1) 2  2) 5   3) 3   4) 5   5) 4   6) 4   7) 2   8) 5   9) 2   10) 3   11) 1  12) 4  13) 2   14) 3    15) 4   16) 4   17) 4   18) 1     

 

Part-2

Directions (Q.1-5): Study the following graph carefully and answer the questions below that
         The following graph shows the speeds (in kmph) of three trucks on different routes on different days of the week.
                                   

1. If the distance travelled by Truck A on Friday was 580 km, what was the time taken by it to travel that distance?
Ans: 11 hr. 36 min.
Explanation:
                             
2. What is the average speed of Truck C in metre per second for all the days together?
Ans: 14.58
Explanation:
                       

3. If the distances travelled by Truck B and Truck A on Tuesday were the same, what was the ratio of the time taken by Truck B to that by Truck A to travel that distance?
Ans: 11:12
Explanation:
Speeds ratio of B and A = 60:55 = 12:11
Times ratio is 11:12 ( Speed and time are inversely proportional)

4. What is the percent increase in the speed of Truck C on Tuesday from the previous day?
Ans: 75%
Explanation:

5. In which of the following days was the speed of Truck A same as the Speed of Truck B on Saturday?
1) Tuesday                  2) Thursday           3) Friday 
  4) Monday                5) None of these
Ans: Monday

Directions (Q.6-10): Study the following pie chart carefully and answer the questions accordingly
Following pie chart gives the percentage of students studying different specializations and the table gives the ratio of men and women in each specialisation in a management college. The total number of students in the college is 4500.

 
                            
6. What is the total number of men studying in the college?
Ans: 2421

Explanation:

Men studying in Marketing = 420
Men studying in I.B. = 675
Men studying in Banking = 340
Men studying in I.T. = 315
Men studying in Finance = 275
Total number = 2421

7. Number of women studying Marketing is approximately what percent of the total number of students in the college?
Ans: 7
Explanation:

8. What is the total number of men studying Banking and International Business?
Ans: 1215
Explanation:

9. Number of women studying Finance is what percent of the number of men studying the
same?
Ans: 80%
Explanation:

10. In which specialisation do the maximum number of women study?
Ans: IT

Directions (Q. 11- 15): Study the following graph carefully and answer the questions given below it.

Following graph gives the Percent Rise in profit of two companies A and B over the years.
                                 

 

11. If the profit earned by company B in 2006 was Rs.1.6 lakhs, what was the profit earned by the company in the year 2007?
Ans: 2.08 lakhs
Explanation:


 

12. What is the average percentage rise in the profit of the company A over all the years together (rounded off to two digits after decimal)?
Ans: 27.14
Explanation:  Average percent rise of company A
                         

 

13. What was the approximate percentage decrease in the percent rise in profit of Company B in the year 2008 from the previous year?
Ans: 16%
Explanation:


14. If the profit earned by company A in 2005 was 2.99 lakhs, what was the amount of profit earned by it in the year 2003?
Ans: 2 lakhs  

Explanation: Let the profit of company A in 2003 be 'x' lakhs.
                            

 

15. What is the respective ratio between the percent rise of company B in 2006 and the percent rise of company A in 2003?
Ans: 7:3
Explanation: Required ratio = 35:15 = 7:3

Directions (Q.16 - 20): Study the following pie chart and table carefully and answer the questions accordingly.

     The Pie-chart shows the distribution of Two lakh candidates who appeared for a Bank Examination from seven states. The table shows the state wise percentage and ratio of male and female qualified candidates

16. What is the number of female candidates qualified from state G?
Ans: 3696 
Explanation:

 

17. What is the ratio of male candidates qualified from state B to state D?
Ans: 122:115
Explanation:

 
18. The number of qualified female candidates from states D, E and F constitute approximately what percent of the total candidates qualified from these states?

Ans: 47%
Explanation:


19. What is the total number of qualified male candidates from states A and C together?

Ans: 15810
Explanation:
 
                            
20. What is the percentage of candidates that have not qualified from states A and B together?

Ans: 44.45%

Explanation:

BIOS

        Acronym for basic input/ output system. It is a set of instructions stored in Read Only Memory (ROM) that lets your computer's hardware and operating system communicate with application programs and peripheral devices such as hard disks, printers and video adaptors.
BIOS extensions
          In the PC, extensions to the main BIOS that enable the computer to work with add-on devices, such as hard disk controllers and EGA or VGA adaptors. The ROM chips containing these extensions do not have to be located on the motherboard; they can also be on expansion boards plugged into the expansion bus. Any BIOS extensions needed to run these expansion boards are loaded automatically when you boot your computer.
BIOS parameter block
          It is a part of the boot record contained on every formatted disk that contains information about the disk's physical characteristics. This information includes the version number of the operating system used to format the disk, the number of bytes per sector, the number of sectors per cluster, per track and per disk, and is provided for use device drivers.
ABIOS
        Acronym for Advanced Basic Input/ Output System. A set of firmware service routines built into the IBM PS/2 series of computers that use the Micro Channel Architecture (MCA) to support multitasking operating systems such as OS/2.
Address
1. The precise location in memory or on disk where a piece of information is stored. Every byte in memory and every sector on a disk have their own unique addresses.
2. To reference or manage a storage location.
Address bus
        The electronic channel, usually from 20 to 32 separate lines wide, used to transmit the signals that specify locations in memory. The number of lines in the address bus determines the number of memory locations that the processor can access, as each line carries one bit of the address.
Absolute addressing
        The explicit specification of memory location by using its address rather than by using an expression from which the address can be calculated. Also known as direct addressing.
Relative addressing
        The specification of a memory location by using an expression to calculate the address, rather than explicitly specifying the location by using its address.
Adaptor
      A printed circuit board that plugs into a computer's expansion bus to provide added capabilities. Common adaptors for the PC include display adaptors, memory expansion adaptors, input/ output adaptors that provide serial, parallel, and games ports, and other devices such as internal modems, CD-ROMs, or network interface cards. One adaptor can often support several different devices; for example, an input/ output adaptor may support one parallel port, a games or joystick port, and several
serial ports.
Accelerator board
      An add-on printed circuit board that replaces that main processor with a higherperformance processor, so you can upgrade your system without replacing monitor, case, keyboard, and so on.
        Using an accelerator board can reduce upgrade costs substantially.
However, there are other factors to consider, such as disk access time, in determining the overall performance of your system.
Graphics accelerator board
         Aspecialised expansion board containing a graphics coprocessor as well as all the other circuitry found on a video adaptor. By offloading most of the graphics processing tasks from the main processor onto the graphics accelerator board, you can improve the performance of your system considerably, particularly if you are a Microsoft Windows user.
Access
         To retrieve data from a storage device such as a hard disk, or to login to a computer system or network.
Access denied
         In DOS, an error message indicating that your last command attempted to act on a file or directory in a way that DOS does not allow.
        You will see this error message if you use a DOS command to try to change or delete a read - only file (A file that had the read-only attribute set), or if you try to copy more files or directories onto a disk than there are directory entries for in the root directory of the disk.
The root directory can only hold a fixed number of file entries (depending on the type of disk). Even though there may be plenty of free space, if there are no more empty entries in the root directory, DOS cannot add your new file and responds with the error message. By the way, this size limitation applies only to the root directory, not to ordinary subdirectories.
Access mechanism
         In a floppy or hard disk drive, the component that positions the read/ write head over the surface of the disk, so that data can be read from or written to the disk.
Access Server
         In networking, a computer that provides access for remote users dialling in, and allows those users to access network resources as though they were working at a computer directly attached to the network. Access servers can be computers designed for this purpose and sold as part of the network, or can be made of multiport CPU cards installed in a PC on the network.
Access time
         The period of time that elapses between a request for information from disk or memory, and the information arriving at the requesting device.
Memory access time refers to the time it takes to transfer a character from memory to or from the processor, while disk access time refers to the time it takes to place the read/ write heads over the requested data. RAM may have an access time of 80 nanoseconds or less, while hard disk access time could be 18 milliseconds or less.
Account
         On local area networks or multi user operating systems, an account is set up for each user. Accounts are usually kept for administrative or security reasons, although in communications and online services, accounts are used as a method of identifying a subscriber for billing purposes.
ACK
         Abbreviation for acknowledgement. In communications, a control code, ASCII06, sent by the receiving computer to indicate that the data has been received without error, and that the next part of the transmission may be sent.
Active-matrix screen
         An LCD display mechanism that uses an individual transistor to control every pixel on the screen.
Active-matrix screens are characterized by high contrast, a wide viewing angle, vivid colours, and fast screen refresh rates, and they do not show the streaking or shadowing that is common with cheaper LCD technology.
Active partition
         That part of the hard disk containing the operating system to be loaded when you start or restart the computer.
         You can install two different operating systems (perhaps DOS and OS/2) on your hard disk, but each must be in its own separate area, or partition. Only one portion can be active at any given time, and to change from the DOS to the non-DOS partition, you may have to use the DOS FDISK command.
Active window
        In an operating system or application program capable of displaying multiple windows on the screen at the same time, the active window is the window that contains the cursor. If a window is active, its title bar changes colour to differentiate it from all the inactive windows. Only one window can be active at a time.

KEEP SOIL ALIVE..  PROTECT SOIL BIODIVERSITY!

1. RBI declared that all branches of Lakshmi Vilas Bank Ltd. operate as branches of DBS Bank India Ltd. from 27 November 2020. Who is the present MD & CEO of DBS Bank India Ltd?
1) Rajesh Prabhu            2) Preeti Priya
3) Surojit Shome            4) Ravindra Bahl
5) Vikram Sud


2. RBI announced to increase the limit for contactless card transactions to…………..from Rs. 2,000 per transaction  from 1 January 2021
1) Rs. 10,000            2) Rs. 15,000
3) Rs. 5,000              4) Rs. 20,000
5) Rs. 25,000


3. As per monetary policy review statement announced by RBI governor on 4 December 2020, Real GDP growth projection for FY 21 revised to ………
1) −7.5%       2) −5.5%       3) −6.5%    4) −8.5%      5) −4.5%


4. The RBI projected CPI inflation at  …………..Q3 of FY 21
1) 4.8%     2) 1.5%     3) 8.4%     4) 3.8%     5) 6.8%


5. Banks can avail funds from RBI   under TLTRO to invest in sectors   under ECLGS 2.0 as per the recent   decision of RBI. In this context what  stands for ‘R’ in TLTRO?
1) Rupee      2) Repo     3) Real    4) Rule     5) Raise


6. Asian Development Bank on 20  November 2020 said it approved $   50 million loan to improve operational   efficiencies and resource  planning and management in…
1) West Bengal           2) Odisha             3) AP
4) Tamil Nadu            5) Chhattisgarh


7. The latest Policy rates and Reserve   Ratios of RBI are given, after declaration   of monetary policy review.   The wrong option is…………
1) Repo Rate : 4.00%     

2) Reverse Repo Rate : 3.35%     

3) Marginal Standing Facility  Rate : 4.25% 

4) Cash Reserve Ratio : 3.00%

5) All of above correct


8. RBI decided to make RTGS available round the clock on all days of the year with effect from …………
1) 25 December 2020
2) 31 December 2020
3) 14 December 2020
4) 14 January 2021
5) 1 February 2021


9. Which international monetary authority promised a loan of $132.8 million loan to Meghalaya to strengthen and modernize the distribution network and improve the
quality of power supplied to households, industries, and businesses on 1 December 2020?
1) AIIB      2) NDB     3) ADB     4) World Bank    5) USAID


10. On 25 November 2020, PM Modi released a special stamp and Rs. 100 commemorate coin on the foundation day of which university/ college/ Institution?
1) Jawaharlal Nehru University
2) Indian Institute of Science
3) IIT Delhi

4) St.Stephen’s College
5) Lucknow University


11. International Day of Banks is observed globally on…………
1) 1 December       2) 8 December
3) 10 December     4) 4 December
5) 11 December


12. World’s first central bank to have over 1 million followers on Twitter is......
1) Sveriges Riksbank, Sweden
2) People’s Bank of China, China
3) RBI, India
4) BangkoSentral ng Pilipinas,Philippines
5) State Bank of Pakistan, Pakistan


13. USA President-elect Joe Biden named whom as his nominee for treasury secretary? If confirmed by the Senate, she would be the first woman ever to hold the post.
1) Janet Yellen           2) Mala Adiga
3) Neera Tanden        4) Jen Psaki
5) Kate Bedingfield


14. RBI ordered which bank to suspend planned digital launches and the addition of fresh credit card customers, following frequent outages in online services ?
1) SBI      2) RBL Bank     3) HDFC Bank   4) YES Bank     5) Union Bank of India


15. To empower MSMEs with instant   digital loans, Suryoday Small  Finance Bank announced partnership  with…………….
1) Amazon Pay       2) Mobikwik       3) PhonePe   

4) G-Pay                 5) Paytm


16. ‘Ek Parivar Ek Bank’ is the punch   line of ……………
1) Bank of India        2) Dhanlaxmi Bank          3) Punjab National Bank

4) ICICI                     5) Bank of Maharashtra


17. Which international monetary organization  allocated $20.3 million aid  to its developing member countries  to access coronavirus vaccine on  17 November 2020?
1) AIIB     2) IDA    3) ADB   4) NDB    5) IMF


18. Who is the chairman of Indian Oil  Corporation appointed as the first  Vice-president of World Liquefied  Petroleum Gas Association  (WLPGA)?
1) PVG Menon                    2) Rajiv Jalota   3) Shrikant Madhav Vaidya
4) Akshay Kumar Singh      5) Sanjay Kumar Mishra


19. BRICS Economic Research Award   2020, declared by EXIM Bank  India conferred on……….
1) Dr. Dinesh Katre
2) Dr. Adam Yao Liu
3) Mark Carney

4) Seema Gupta
5) Aditya Puri


20. Which two nations are the biggest  contributors towards FDI equity  inflows to India as per the data  published by the Department for  Promotion of Industry and  Internal Trade (DIPP) between April and September 2020?
1) UK and USA
2) France and USA
3) Singapore and USA
4) Singapore and Mauritius
5) USA and Japan


21. Which day celebrated as ‘Awaas Diwas’ to commemorate the launch of PMAY-G, which aims to provide “Housing for All” by 2022?
1) 1 December       2) 14 December    3) 20 November

4) 30 November     5) 5 December


22. Which railway station renamed as  Mahadevappa Mailara Railway  Station in Karnataka?
1) Raichur                         2) Mandya     3) Haveri
4) Subramanya Road        5) Hassan


23. Who launched ANANDA (Atma Nirbhar Agents New Business Digital Application), a digital application for agents for onboarding to get a life insurance policy?
1) SBI Life                        2) HDFC Life      3) LIC
4) ICICI Prudential Life    5) Sri Ram Life Insurance


24. On 25 November 2020, who  launched the Securities Market  Trainers (SMARTs) program, an  initiative aimed at enhancing investor education and awareness?
1) RBI         2) BSE       3) NSE
4) SBI         5) SEBI


25. On 1 December 2020, which state  launched the biggest-ever DirectBenefit Transfer (DBT) scheme  called 'Orunodoi', aiming to cover 22 lakh families by transferring  Rs. 830 per month to the account  of one of the female members of the family?
1) Odisha    2) UP   3) West Bengal   4) Tamil Nadu   5) Assam


26. Uday Shankar was elected as the  new president of …………..
1) FICCI   2) NHB   3) ASOCHAM  4) CII   5) Exim Bank


27. Which North Eastern state was  conferred with four awards for its  more success in the fishery sector  by National Fisheries Development  Board?
1) West Bengal   2) Andhra Pradesh   3) Assam           

4) Maharashtra   5) Karnataka


28. Which nation declared a climate emergency on 2 December 2020 and pledged that its public sector would become carbon neutral by 2025?
1) USA    2) Russia  3) New Zealand 4) Norway  5) Sweden


29. Government of India appointed whom as the new Chairperson of National Dairy Development Board (NDDB)?
1) PD Vaghela   2) Varsha Joshi
3) Sahil Seth     4) Abhas Jha
5) SN Shrivastava


30. Union government unveiled which scheme to impart training to primary cooperative societies in rural areas on 24 November 2020?
1) Sahakar Pragya   2) ARYA    3) Deendayal Antyodaya Yojana
4) ASPIRE               5) Nai Udaan


31. Who is Comptroller & Auditor General of India, elected as External Auditor of Inter Parliamentary Union (IPU), Geneva for a three-year term.
1) K K Venugopal
2) Pradeep Kumar Joshi
3) Girish Chandra Murmu
4) Harsh Vardhan Shringla
5) Desh Deepak Verma


32. India gets which rank in the renewable power capacity as per the statement given by PM Modi in the RE-Invest 2020 meet on 26 Nov 2020?
1) 2nd   2) 7th    3) 10th    4) 4th    5) 8th


33. "Keep soil alive, protect soil biodiversity" is the theme of World Soil Day observed on…
1) 5 December     2) 10 December
3) 7 December     4) 1 December
5) 3 December


34. Uttar Pradesh Cabinet cleared the proposal to rename which airport as Maryada Purushottam Sri Ram Airport?
1) Ayodhya    2) Lucknow    3) Mathura
4) Varanasi    5) Shravasti


35. Government of India is working on an idea to set up a refinery for production of aviation fuel from bamboo grown in the Gadchiroli district of………….
1) Karnataka    2) Maharashtra
3) Jharkhand   4) Arunachal Pradesh
5) Tripura


36. NITI Aayog formed a panel to study feasibility of hyperloop technology in India under the chairmanship of………..
1) Ajay Bhushan Pandey
2) Krishnamurthy Subramanian
3) Karnal Singh

4) VK Saraswat
5) Vinod Kumar Yadav


37. Reliance Industries got first rank in the Fortune 500 list of Indian firms. Which company got second rank?
1) ONGC   2) TATA Motors   3) IOC   4) TCS   5) ICICI Bank


38. Which Municipal Corporation bonds on 2 December 2020, became the first municipal bonds from North India listed on Bombay Stock Exchange?
1) Mumbai    2) Delhi    3) Lucknow   4) Kolkata    5) Pune

 

Key

1-3     2-3      3-1      4-5    5-2    6-1    7-5    8-3    9-3    10-5    11-4    12-3    13-1    14-3    15-5    16-5    17-3  18-3    19-2    20-3    21-3    22-3    23-3    24-5    25-5    26-1  27-3    28-3    29-2    30-1    31-3   32-4    33-1    34-1    35-2    36-4    37-3    38-3

SIMPLE INTEREST

SOLVED EXAMPLES

Example 1 :
If the simple interest on Rs. 1500 increases by Rs. 30. When the time increases by ‘8’ years. Find the rate of interest per annum.
   (1) 0.5%       (2) 0.25%     (3) 0.75%     (4) 1.25%     (5) None of these
Sol. (2) Initially

 

Example 2 :
Rajiv took a loan at simple interest rate of 6% in the 1 year with an increase of 0.5% in each subsequent year. She paid interest of Rs. 3375 after 4 years. How much loan did she take.
   (1) 15800      (2) 12500    (3) 33250   (4) 15600    (5) None of these
Sol. (2) Total paid interest = 3375
              Rate = 6% and increasing by 0.5% every year.
              Let total taken amount = P

 

Example 3 :
Raju invested an amount Rs. 3000 at the simple interest rate 2 1/2 %of percent per annum and another amount at the simple interest rate 5% p.a. The total interest earned at the end of   year on the total amount invested scheme 3 1/2 % p.a. Find the total amount invested.
(1) 2000 (2) 4000 (3) 5000 (4) 3500   (5) None of these
Sol. (3)
     
   ⇒  15000 + 10x = 7x + 21000
  ⇒ 3x = 6000  ⇒ x = 2000
     Total x+ 3000 = 5000
Alternate Method :
   
     x1 and x2 are deposits
     ⇒ 3000 × 5 + 10 x2 = 21000 + 7x2
     ⇒  x2 = 2000
     Total = 3000 + x2
    3000 + 2000 = 5000

 

Example 4 :
Rs. 800 becomes Rs. 956 in 3 yrs at certain simple interest rate of interest. If the rate of interest is increased by 4. What amount will Rs. 800 become in 3 years.
  (1) 1020     (2) 1025     (3) 1052    (4) 1010   (5) None of these
Sol. (3) P = 800, A = 956
               SI = A – P = 956 – 800 = 156
               T = 3 Yrs
             
             New rate = 6.5 + 4 = 10.5%
           
            Amount = P + SI = 800 + 252 = 1052

 

Example 5 :
What annual payment will discharge a debt of Rs. 5600, due 5 years hence at  the rate of 6% simple interest.
    (1) 500       (2) 560     (3) 1000      (4) 750           (5) None of these
Sol. (3)

 

EXERCISE

1. Rakesh borrowed some money at the rate of 7% p.a. for the 1st 3 years, 9% p.a. for the next 6 years and 10% p.a. for the period beyond 9 years. If the total interest paid by him at the end of 15 years is Rs. 4050. How much money did he borrow.
A: 3000
Solution:
Let his deposit                 = 100
Interest for 1st 3 years    = 21
Interest for next 6 years = 54
Interest for last 6 years   = 60
                                           135
Total interest = 135
When interest ‘135’ deposit amount is Rs. 100.
Therefore when interest is 4050, deposited amount =

 

2. A certain sum is invested for certain time. It amounts to Rs. 60 at 6% per annum. But when invested 3% p.a. It amount to Rs. 30. Find the time.
A: Not possible
Solution:
Amount = P + SI :   Amount = P + SI
SI = 60 – P           :   SI = 30 – P

 

3. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 5% higher rate, it would have fetched Rs. 125 more. Find the sum.
A: 1250
Solution:
    Let the sum = Rs. x
    Rate of interest = y%
     New rate of interest = (y + 5)%
    
        ⇒   10x = 12500
  ⇒   x = 1250
Alternate Method :

  Sum = Rs. 1250
  A = 125, T = 2, x = 5.

 

4. The simple interest on a sum of money will be Rs. 400 after 3 years. In the next 3 years, principal becomes 4 times. What will be the total interest at the end of the 6th year.
A: 2000
Solution:
    
    SI for next 3 years


    
     Total SI at the end of 6th year = 400 +1600 = 2000
Alternate Method :
Interest = (n + 1)x               n = 4, x = 400
               = (4 + 1)400
               = 5 × 400 = 2000.

5. Certain amount 10 times in 15 years. In how many years it become 28 times on simple interest?
A: 45 yrs
Solution:
   Let the S.I = A – P = 10 P – P = 9P
  
   R = 60%
   SI = 28P – P = 27 P

6. A sum of Rs. 2600 is lent out in 2 part in such a way that the interest on one part at 10% for 5 yrs is equal to that another part is 9% for 6 years the sum lent out at 10% is ?
A: 1350
Let the sum one part is Rs. ‘x’ at 10% in 5years
Another part is Rs. (2600 – x) at 9% in 6 years
From question

⇒ 50x = 2600 54
⇒ x = 1350

Alternate Method :
            2600
10%                        9%
5yr =50              6yr = 54
LCM of 50, 54 = 270
The ratio = 54 : 50

 

7. A certain sum of money amounted to Rs. 1020 at 9% in a time in which Rs. 720 amounted to Rs.880 at 4%. If the rate of interest is simple. Find the sum.
A: 680
Solution:

 

8. Rs. 7914 is divided into three parts in such away that the first part at 3% per annum after 8 years, the second part 4% per annum after ‘5’ years and third part at 6% per annum after ‘2’ years give amount find each part.
A: 2515, 2714, 2614
Solution:

9. Venu invested a sum of money at a certain rate of interest for a period of 4 years had he invested the same sum for a period of 6 years the total interest earned by him would have been fifty % more that the earlier interest amount. What was the ratio of interest percent per annum.
A: can’t be determined
Solution:

10. A certain sum of money at SI amounts to Rs.1012 in 2 1/2 % years and to Rs.1067.20 in 4 years. The rate of interest per annum is
A: 4%
Solution:

L.C.M AND H.C.F

Factor: one number is said to be a factor when it divides the other number exactly. Thus 3 and 4 are factors of 12
Multiple: one number is said to be a multiple of other number when it is exactly divisible by the other.
Common factor: A common factor of two or more numbers is a number that divides each of them exactly. Thus 4 is a common factor of 12,16,24,72
Common multiple: A common multiple of two or more numbers is a number which is exactly divisible by each of them. Thus 18 is a common multiple of 2,3,6 and 9.
Highest Common Factor (HCF): HCF of two or more given numbers is the greatest number that divides each of them exactly. Thus 5 is the HCF of 25 and 35.
HCF is also called Highest Common Divisor or Greatest Common Divisor.
Methods to find HCF
Method of prime factors: Break the given numbers into prime factors and then find the product of the prime factors common to all the numbers. This product will be the required HCF.

Example: HCF of  20, 35 and 45 is                                   
                                       20  =  2 × 2 × 5
                                       35  =  5 × 7
                                       45  =  3 × 3 × 5
     The factor common to all the numbers is 5, hence 5 is the HCF.
Method of Division: Divide the greater number by the smaller number, if there is remainder then divide the divisor by the remainder, if again there is remainder, then again divide the divisor by the next remainder and so on until no remainder is left. The last remainder is the required HCF.
Methods to find LCM
Method of prime factors: Divide the given numbers into their prime factors and then find the product of the highest powers of all the factors that occur in the given numbers, and this product will be the required LCM.
Example: LCM of 4, 8 and 24 is
                                          4   =  2 × 2                =  22
                                          8   =  2 × 2 × 2         =  23
                                          24 =  2 × 2 × 2 × 3  =  23 × 3
      The prime factors that occur here are 2 and 3. the highest powers of these prime factors are 23 and 31 respectively.
      Therefore the required LCM  is 23 × 31 = 24.
Regular method: Write all the given numbers in a line and divide them by a number which will exactly divide at least any two of the numbers. write down the quotients and the undivided numbers in a line below the first. Repeat the process until we get a line of numbers which are prime to each other. The product of all the divisors and the numbers in the last line will be the required LCM.
Example:
 LCM of 8, 12 and 32 is

Therefore required LCM is  2 × 2 × 2 × 3 × 7 × 4 = 672
LCM of decimals: First find LCM of the given numbers without decimals and then put the decimal in the result after the number of digits which is equal to the minimum digits after the decimal in the given numbers from right to left.
Example:
                 LCM of 2.4, 0.012  and 0.32 is 
                 LCM of 24, 12 and 32 is 96
In the given numbers the minimum digits from right to left is in 2.4 i.e., 1
Therefore the required LCM  is 9.6.



 

AVERAGES


Examples

Example 1. A batsman has a certain average runs for 16 innings. In the 17th inning he made a score of 85 runs thereby his average is increased by 3. What is his average after 17th inning?
Sol: The average for 17th inning has been increased by 3.
 The total increase in the runs for 17th inning = 17 × 3 
                                     = 51
 But the batsman scores 85.
 Average runs in his 16th innings = 85 -51 
                            = 34.
 Hence the average of runs after 17th innings = 34  + 3 
                                                = 37
Example 2.  A man has 7 children. When their average age was 12 years, the child who was 6 years of age, died. What was the average age of surviving children 5 years after the death of the above child?
Sol: Average age of 7 children  = 12 years
Total age of 6 children  =  12 × 7 = 84 years
Total age of 6 children after the death of a child aged 6 years = 84- 6 = 78
Hence   the average age of the surviving children = 
After 5 yrs. = 13 + 5 = 18 yrs.
Example 3.  If the weights of 5 students of a class are 49.6 kg, 39.8 kg, 45.2 kg and 24.6 kg respectively then what is their average weight?
Sol: Total weight of 5 students = 49.6 + 39.8 + 40.8 + 45.2 + 24.6
                      = 200 kg.
Their average weight =  
                    = 40 kg.
Example 4.  The average temperature for Monday, Tuesday and Wednesday was 36ºC  . The average temperature for Tuesday, Wednesday and Thursday was. If the temperature for Thursday was 37ºC, what was the temperature on Monday?
Sol:   Average temperature for Monday, Tuesday and Wednesday = 36ºC
Total temperature for Monday, Tuesday and Wednesday = 36 × 3 
                                          = 108ºC
Average temperature for Tuesday, Wednesday and Thursday = 38ºC
Total temperature for Tuesday, Wednesday and Thursday = 38 × 3 
                                           = 114ºC  
Total temperature for Tuesday and Wednesday only = 114 - 37 
                                     =  77ºC
Temperature for  Monday only = 108 – 77 
                         = 31ºC
Example 5.  A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.

Example 6.  A vehicle travels from A to B at the speed of 40 km/hr, but from B to A at the speed of 60km/hr. what is its average speed during the whole journey?
Sol: Let the distance from A to B be x km


Example 7.  The average age of a class of 40 boys is 16.95 years. A new boy joins the class and the average age now is 17 years. What is the age of the new boy?
Sol:  The average age of 40 boys  = 16.95 years
                Total are of 40 boys  = 16.95 × 40
                                 = 678 years
        The average age of 41 boys  = 17 years
                Total age of 41 boys  = 17 × 41
                                = 697 years
                 Age of the new boy  = 697 – 678
                                = 19 years

(Writer - G.S.Giridhar)

PERCENTAGES

         A fraction with denominator 100 is called percentage. Numerator of that fraction is called rate percent.
The term percent means per every 100.
50 percent means 50 out of 100.
The symbol  % is used to denote percent. Ex: 20%, 35%, 80% etc.
Percent to fraction: To convert percent into fraction, divide the percent by 100.

Fraction to percent: To convert fraction into percent, multiply the fraction by 100.

Increment percent = 
Ex: increment % in 5 and 8  is  3/5  × 100 = 60%.
Decrement percent  =  
Ex. Decrement % in 5 and 8 is 5/8  × 100 = 37.5%. 
Some important percent /fractions.

             Following rules should be kept in mind for solving the questions on percentage
1. For converting a given percentage into a fraction, divided it by 100 or multiply by 
2. For converting a given fraction into a percentage multiply it by 100.
3. For converting one given quantity, say, x as a percentage of another given quantity, say, y find 
   Note - percentage is never expressed in any unit like rupees or kilos.
4. When there are two articles ‘a’ and ‘b’ in a group and in the ratio of a : b then to express any one article as a percentage of the group, divide the article by the total articles of the group and multiplies the whole by 100.
Percentage of ‘a’ = 
And, Percentage of ‘b’ = 

EXAMPLES

Example 4. How many percent is 15 cm of 1 metre?

Note: Both quantities are converted into same unit.
Example 5.  A person spent 85% of his monthly income and thereafter saves Rs.360 per month. Find out his total income.
Sol: Suppose his monthly income is Rs. 100
Expenditure = 85% = Rs. 85
Saving = Rs. 100 – 85 = Rs. 15
If saving is Rs. 15 income is Rs. 100
If saving is Rs. 360 income is  
                                                 = Rs. 2400
Example 6. If a student gets 38 marks out of 50, what is the percentage of his obtained marks?
Sol:  Percentage of obtained marks  
                                                                = 76%
Example 7.  If two numbers are respectively 30% and 40% more then a third number, what percentage is the first of the second?
Sol: Let the third number be 100
          First number  = 100 + 30% of 100
                                = 130
 and Second number   = 100 + 40% of 100
                                = 140
  Percentage of the first number to the second number to the second number 

Example 8. A student scores 20% marks and fails by 30 marks while another student who scores 32% marks, gets 42 marks more than the minimum required pass marks. What are the maximum marks for the examination?
Sol:   32% - 20% = 12%
      And 42–(-30) = 72
       12% marks = 72          
    100% marks = 
Example 9.  An engineering student has to secure 50% marks to pas. He gets 163 marks and fails by 37 marks. Find the maximum marks
Sol: Minimum marks required = 163 + 37  = 200
         If 50 are the minimum marks then maximum marks  = 100
    200 are the minimum marks then maximum marks =                                                                                                                
 

Profit & Loss

The money spent to purchase an article is cost price of the article, and the money received for selling an article is called selling price.
                               Profit = selling price – cost price
                                Loss = cost price – selling price

Profit or loss percent is always calculated on C.P unless it is required to calculate on S.P.

DISCOUNTS
        The price at which the article is marked is the marked price or listed price or labeled price or catalogue price.
        The discount is allowed on marked price for the cash payments.
                    
       When discount is deducted from the marked price, the remainder becomes the selling price.
       To find Marked price from Cost Price we can use the following formula
                   
EXAMPLES

Example 1.   Ram sold a cow for Rs.136 at a loss of 15%. At what price should he have sold it to gain 15%?
Sol: Let the cost price be Rs.100 then for 15% loss the S.P = 85 and for 15% profit it should  be Rs. 115.
         Rs. 85 is the first S.P, then second S.P. = Rs. 115
         Rs. 136 is the first S.P =  
Example 2.   A sells a radio to B at a gain of 10% and B sells it to C at a gain of 5%.If C pays Rs. 462 for it, What did it cost to A?
Sol: Let the cost price of A be Rs. 100
        Then the cost price of B be Rs. 110 
         
         
Example 3. A dealer allows 10% discount on the list price of a certain article and yet makes a profit of Rs. 25% on each article. Find the cost price of the article when list price is Rs. 50.
Sol:  Let the cost price of articles be Rs. 100
          Then for 25% profit, S.P.  = Rs. 125
          If list price is Rs. 100, S.P.  = Rs. 90
          If S.P. is Rs. 90, list price  = Rs. 100
          
       Example 4. A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. Had he sold all of them at a uniform profit of 15% he would have got Rs.40 less. Find the cost price of each clock.
Sol: Let the C.P of clock is Rs. 100 each.
        By the profit of 10% S.P. of 40 clocks =  = Rs. 4, 400
        By the profit of 20% S.P of 50 clocks =   = Rs. 6, 000
        Total S.P. = Rs. 4400 + Rs. 6, 000 = Rs. 10, 400
        C.P of 90 clocks =   = Rs. 9000
        By the profit of 15% S.P. of 90 clocks =   = Rs. 10, 350
        Difference = Rs. 10, 400 – Rs. 10, 350 = Rs. 50
        If the difference is Rs. 50 then C.P. = Rs. 100
        If the difference is Rs. 40 then C.P. =  = Rs. 80

Example 5.  A man buys 5 horses and 10 cows for Rs. 1,600. He sells horses at a profit of 15% and cows at a Loss of 10% if his over all profit was Rs. 90, what was the cost price of a horse and a cow?
Sol:  Let x be the cost price of a horse and y be the cost price of a cow
          C.P. of 5 horses = Rs. 5x and C.P of 10 cows = Rs. 10y
        Hence     5x + 10y = 1,600……..(i)
        Since the profit is 15% on the horses  
        
            

 

Sentence Improvement

Directions: In the following questions, a sentence or a part of a sentence is printed in bold. Below are given alternatives numbered 1, 2, 3, 4 to the bold part of the sentence which may improve the sentence. If you think that the sentence is correct as it is, choose (5) as your answer.
(SBI CLERICAL MAIN 2014)
1. The oak tree always/thought that/he was strong/than any other tree in the garden.
1) The oak tree always 2) thought that
3) he was strong 4) than any other tree
5) No correction required
2. It was strange /when people started/congratulating me/on completion of my dissertation.
1) It was strange 2) when people started
3) Congratulating me 4) On completion of my dissertation
5) No correction required
3. A good employee/is one which/ is always willing/to the extra mile.
1) A good employee 2) is one which
3) is always willing 4) to go the extra mile
5) No correction required
4. Through her efforts/she managed to/ open several institutions to/ help the downtrodden.
1) Through her efforts 2) she managed to
3) open several institutions to 4) help the downtrodden
5) No error
(SBI ASSISTANT EXAM 08/2014)
5. The Indian political class is known for engaged themselves in socio-economic development of society.
1) known for engaging 2) call for engaged
3) knowing for engaging 4) called for engaging
5) no correction required
6. The launch of metro service in the city, has enhancing public transport options.
1) have enhanced 2) has enhanced
3) has been enhanced 4) had enhanced
5) no correction required
7. As houses grow and parking areas shrink, more than a little people have expressed their scorn for trees
in the capital, one of the world's greenest.
1) more little people 2) much little people
3) more than a few people 4) much than a few people
5) no correction required
8. Rare Indian art spanning a period from the eighth century to the twentieth century will be up for sale
at an auction later this month.
1) art span a period from 2) art spanning a period
3) a period of art spanning from 4) a spanning art of
5) no correction required
9. Other species of eel are also faced various level of threats due to habitat damage and overfishing.
1) facing various threat 2) facing various level of threats
3) faced with various levels of threatening 4) face various levels of threats
5) no correction required
(SBI CLERKS EXAM 06/2012)
10.
 They are yet to decided about buying the new furniture.
1) still decide 2) yet to decision
3) yet to decide 4) still decided
5) no correction required
11. Rohan's mother was feed up of his laziness.
1) fed up in 2) fed off 3) feeds up of 4) fed up of
5) no correction required
12. She was just looking outside the window when a beautiful bird caught the eye.
1) catch the eye 2) eye catching
3) caught her eye 4) catch her eyes
5) no correction required
13. They sent out the invitations last evening.
1) send out 2) sending out 3) sent at 4) sending in
5) no correction required
14. He had to bear the brunt of his father's mistakes.
1) bore the brunt 2) bear the burns
3) bear a brunt 4) bear and burn
5) no correction required
(SBI CLERICAL MAIN EXAM 2012)
In each question below, four words printed in bold are given. Mark the number of the word that is inappropriate or wrongly spelled as your answer. If you think that all the words are correctly spelt and appropriate in the context of the sentence, then mark "No error" as your answer.
15. Ronald was very proud (1)/ of his new car would always (2)/ be on the look out for an excuse (3)/ toflaunt (4) it/. No error (5)/.
16. Ramesh had an aversion (1)/ to alcohol and would (2)/ avoid going to partyes (3)/ with his friends (4)/. No error (5)/.
17. Lucy was working (1)/ overtime because (2)/ she had to prepare (3)/ for an important meating (4)/. No error (5)/.
18. Roshni was found (1)/ of pets and she was a proud (2)/ owner of many unique (3)/ animals (4)/. No error (5)/.
19. Ahmad was not only very intelligent (1)/ but also very sincere (2)/ and would always strand (3)/ first in his class (4)/. No error (5)/.
20. His proposal (1)/ had to be send (2)/ to the President of the company (3)/ for her approval (4)/. No error (5)/.
Directions: In the following questions, a sentence or a part of a sentence is printed in bold. Below are given alternatives numbered 1, 2, 3, 4 to the bold part of the sentence which may improve the sentence. If you think that the sentence is correct as it is, choose (5) as your answer.
21. Your bonus will dependent the quality of your work
1) is dependable 2) depends on
3) being dependent 4) is going to depend
5) no correction required
22. Even after talking the matter for hours, we could not arrive at a decision.
1) talking to 2) talking over
3) talked about 4) talk through
5) no correction required
23. Mr Gates is a successful entrepreneur donated most of his wealth to charity.
1) has donated most of 2) donated mostly
3) donates much of 4) who has donated most of
5) no correction required
24. The government is unwilling to make any concession to their demands.
1) not willing to take 2) willingly given
3) not willing in giving 4) unwilling to take
5) no correction required
25. If the accused was guilty for the crime, he should be punished.
1) was guilty in 2) has been guilty for
3) was in guilty of 4) is guilty of
5) no correction required
26. The officer suffered only because of his impolitely behaviour
1) behaviour was impolite 2) behaved impoliteness
3) behavioural impolite 4) impolite behaviour
5) no correction required
KEY
1-3, 2-1, 3-2, 4-1, 5-1, 6-2, 7-3, 8-5, 9-2, 10-3, 11-4, 12-3, 13-5, 14-5, 15-5, 16-3, 17-4, 18-1, 19-3, 20-2, 21-2, 22-3, 23-4, 24-3, 25-4, 26-4.

EXPLANATIONS
1. 
Correct the adjective 'Strong'as 'Stronger' to write the sentence in the comparative Degree.
2. Correct it as 'It is strange' It is a usage.
You can also say 'it seems strange' when talking about how you feel when you arrive at a new place or face a new situation.
3. Replace 'Which' with 'Who'. An employee is a person, not a lifeless thing. Here is the car which I bought last year.
4. Replace 'Through' with 'by/with'
16. Correct it as 'PARTIES'. The plural of Countable Nouns which end in '-EY' is formed only by adding '-S' to the Singular like 'Monkeys' and 'Storeys'.
17. Replace 'Meating' with 'Meeting'.
18. Correct the 'Found' as 'Fond' which means 'To like someone or something very much'.
19. Correct the word, 'Strand' as 'Stand'. One of the meanings of the word, 'Strand' as a Noun is, 'A thin thread of something'.
20. Correct the verb, 'Send' as 'Sent'. The Main Verb after the 'Be' form verbs (am, is, are, was, were, being, been and be) is normally used in the 'V3' form. (e.g.: Take-took-taken).
23. The Relative Pronoun ‘Who’ is needed to connect the second part of the sentence. Writer: M. Somasekhara Prasad

Parts of speech

Fill in the blanks with words

Pronouns:
1. The landlady gets ------ clothes pressed in paris.

2. 'We have occupied ------ seats. Have ------- occupied ------?'
3. I got ------ aching tooth extracted.
4. The person ----- sells meat is a butcher.

 

Answers: 1. her     2. our, you, yours      3. my      4. who

 

Adverbs:

1. He spoke with great eloquence. He spoke ------
2. I thank you with all my heart. I thank you -------
3. The soldiers fought with great courage. They fought very -------
4. She searched for her umbrella in all places. She searched for her umbrella ------

 

Answers:   1. eloquently      2. wholeheartedly       3. courageously        4. everywhere
 

Adjectives:
1. I am ----- than Shahbuddin. (elder/ older)

2. We tuned on the radio for the ------ news. (latest/ last)
3. Gold is one of the ------ of metals. (costly)
4. Preethi is ------ than her elder sister. (tall)

 

Answers: 1. older        2. latest        3. costliest      4. taller

 

Verbs:
1. We ------ children's day last month. (celebrate)

2. I ---- the book tomorrow. (return)
3. It ------ since yesterday. (rain)
4. Vaseema ---- in IX class last year. (be)

 

Answers: 1. celebrated      2. will return      3. has been raining     4. was
 

Conjunctions:
1. I would have stopped ----- I had seen you.

2. Run fast ----- you won't win the race.
3. ------ you ask me, I won't help you.
4. We should not cut down the trees ------- they give us rain.

 

Answers:  1. if       2. otherwise      3. unless      4. since/ as
 

Prepositions:
1. It is ten ------- my watch.

2. There are a number of birds ------ the tree.
3. He is not interested ------- English.
4. My father gave -------- smoking.

 

Answers:  1. by     2. in        3. in       4. up
 

Interjection:
1. ------! We've won the match.

2. ------! The injured were dead.
 

Answers: 1. Hurrah!      2. Alas!

RATIO AND PROPORTION

RATIO: Ratio means Comparison. The number of times one quantity contains another quantity of the same kind.
            Thus the ratio between 5 litres of oil and 15 litres of oil can be possible, but not between 10 apples and 25 kg of rice. 
* The ratio between one quantity to another is measured by  a : b or a/b
Ex: 8 : 9   or   5 : 7 etc.
* The two quantities in the ratio are called its terms. The first is called the antecedent and the second term is called consequent.
* The terms of the ratio can be multiplied or divided by the same number.
Types of Ratios:
1. Duplicate ratio: The ratio of the squares of the two numbers.
     Ex: 9 : 16 is the duplicate ratio of 3 : 4.
2. Triplicate Ratio: The ratio of the cubes of the two numbers.
     Ex: 27 : 64 is the triplicate ratio of 3 : 4.
3. Sub-duplicate Ratio: The ratio between the square roots of the two numbers.
      Ex: 4 : 5 is the sub-duplicate ratio of 16 : 25.
4. Sub-triplicate Ratio: The ratio between the cube roots of the two numbers.
      Ex: 4 : 5 is the sub-triplicate ratio of 64 : 125.
5.Inverse ratio: If the two terms in the ratio interchange their places, then the new ratio is inverse ratio of the first.
      Ex: 9 :5 is the inverse ratio of 5 : 9.
6. Compound ratio: The ratio of the product of the first terms to that of the second terms of two or more ratios.
      Ex: The compound ratio of   
PROPORTION: If two ratios are equal, then they make a proportion.
            Thus  
Each term of the ratios   is called proportional.
The middle terms 5 and 8 are called means and the end terms 4 and 10 are called extrems.d
Product of Means = Product of Extremes


Continued Proportion: In the proportion    8, 12, 18 are in the continued proportion.
Fourth proportion: If a : b = c : x, then x is called fourth proportion of a,b and  c.
There fore fourth proportion of  a, b, c  = 
Third proportion: If a : b = b : x, then x is called third proportion of a and b.
Therefore third proportion of a, b =  
Second or mean proportion: If a : x = x : b , then x is called second or mean proportion of a and b.
Therefore mean proportion of a and b =  
1. a : b = 3: 4; b : c = 6 : 7. Find a : b : c.
Sol:    a     b      c
          3     4
                 6      7
a : b : c = 3 × 6 : 6 × 4 : 4 × 7 = 9 : 12 : 14
2. A sum of Rs.4960 has been divided among A, B and C in the ratio of 5:4:7. Find the share of B.
Sol: B's share =  
                          = Rs.1240


3. 36% of first number is 28% of the second number. What is the respective ratio of the first number to the second number?
Sol:  Let the numbers be x and y.
       36% of x = 28% of y
       
          x : y = 7 : 9


4. Two numbers are in 4:7 ratio. The difference between them is 27. What is the bigger number?
Sol:  Let the numbers be 4x and 7x.
             7x - 4x = 27
            3x = 27    x = 9
 Bigger number is 7x = 7 × 9 = 63
Short cut: The difference of the terms of the ratio = 7 − 4 = 3.
 But the actual difference between the numbers is 27 
 3 parts is equal to 27
 7 parts (Bigger number) =  × 27 = 63
5. The ratio of the ages of a man and his son is 7: 3. The average of their ages is 30 years. What will be the ratio of their ages after 4 years?
Sol: Average age = 30 years
Total age = 2 × 30 = 60 years.
Let their present ages be 7x and 3x years
 7x + 3x = 60  x =  = 6
 Their present ages are
7 × 6 and 3 × 6 = 42 and 18.
 Their ages after 4 years
= 42 + 4 and 18 + 4 = 46 and 22 years
 ratio = 46 : 22 = 23 : 11


6. Two numbers are in the ratio of 3:4. If 4 is subtracted from each, the remainders are in the ratio of 5:7. What are the numbers?
Sol: Let the numbers be 3x and 4x.
If 4 is subtracted from each, the numbers will be (3x -4) and (4x -4).
(3x-4) : (4x -4) = 5: 7
Product of means = Product of extremes
(3x-4) 7 = (4x - 4) 5
 21x - 28 = 20x - 20
 x = 8
 The numbers are 3 × 8 and 4 × 8 
                   = 24 and 32


7. In a bowl there is 30 litre mixture of milk and water. The ratio of milk and water is 7:3. How much water must be added to it so that the ratio of milk to the water be 3:7?
Sol : Milk quantity in the mixture
=  ×30 = 21 litres
 Water = 30 - 21 = 9 litres
New ratio = 3 : 7
 3 parts of milk is 21 litres (There is no difference in the milk quantity of new mixture)
 Water quantity in the mixture
=  × 21 = 49 litres
 49 - 9 = 40 litres  water is to be added in the new mixture


8. A bag contains of one rupee, 50 paise and 25 paise coins. if these coins are in the ratio of 5 : 6 : 8, and the total amount of coins is Rs. 210, find the number of 50 paise coins in the bag.
Sol : Let the number of one rupee, 50 paise, 25 paise coins be 5, 6 and 8 respectively
The value of one rupee coins
             = Rs. 1 × 5 = Rs. 5
The value of fifty  paise coins
             = Rs. 0.50 × 6 = Rs. 3
The value of twenty five paise coins
             = Rs. 0.25 × 8 = Rs. 2
Total value = 5 + 3 + 2 = Rs. 10
If the total value is Rs. 10
there are 6 coins of fifty paise
if the total value is Rs. 210, then the number of 50 coins =  × 6 = 126
9. If a sum of Rs.3150 were distributed among Ravi, Vijay and Suresh in the ratio of 12:9:14 respectively, then find the share of Vijay.
Ans: Rs.810
Sol: Vijay's Share =  × 3150 = Rs.810


10. The total number of students in a school is 2850. If the number of boys in the school is 1650, then what is the respective ratio of the total number of boys to the total number of girls in the school?
Ans: 11:8
Sol: Total number of students = 2850
Number of boys = 1650
Number of girls = 2850-1650 = 1200
Ratio between boys and girls
=1650 : 1200 = 11 : 8


11. A sum of money is divided among A, B, C and D in the ratio of 5 : 6 : 12 : 15 respectively. If the share of C is Rs. 4092, then what is the total amount of money?
Ans: Rs. 12958
Sol: Let the share of A, B, C and D be Rs. 5x, 6x, 12x and 15x respectively. C's share is Rs.4092
 12x = 4092   x=  = 341
  Total money = 38x = 38 × 341= Rs.12958


12. Asum of Rs. 2820 has been distributed among A, B and C in the ratio  respectively. What is the share of B?
Ans: Rs. 900
Sol: LCM of 3, 4 and 5 is 60
 ratio =  : 20 : 15 : 12
 B's share =  × 2820
 =   ×2820 = Rs. 900 

13. A, B and C divide an amount of Rs. 6300 amongst themselves in the ratio of 7:6:8 respectively. If an amount of Rs.300 is added to each of their shares, what will be the new respective ratio of their shares of amount?
Ans: 8 : 7 : 9
Sol: Total shares = 7 + 6 + 8 = 21
         21 parts = 6300
       each part =  = 300
 Their shares are
7 × 300, 6 × 300 and 8 × 300
  2100, 1800 and 2400
If 300 is added to each of them then their shares are 2400, 2100 and 2700
Their ratio = 2400 : 2100 : 2700                   
 = 8 : 7 : 9
14.  Find out the two quantities whose difference is 30 and the ratio between them is 5/11.
Sol: The difference of quantities, which are in the ratio 5:11, is 6. To make the difference 30, we should Multiply them by 5.
        Therefore  
15. A factory employs skilled workers, unskilled workers and clerks in the ratio 8:5:1 and the wages of a skilled worker, an unskilled worker and a clerk are in the ratio 5:2:3 when 20 unskilled workers are employed the total daily wages fall amount to Rs. 318. Find out the daily wages paid to each category of employees.
Sol: Number of skilled worker: unskilled worker: clerks = 8:5:1 and the ratio of their respective Wages = 5:2:3
      
Hence the amount will be paid in the ratio 8 × 5 : 5 × 2 : 3 × 1 = 40 : 10 : 3             
Hence total amount distributed among unskilled workers 

But the number of unskilled workers is 20, so the daily wages of unskilled worker 

The wages of a skilled worker, an unskilled worker and a clerk are in the ratio = 5:2:3
Multiplying the ratio by   we get = 7.50 : 3 : 4.50
So, if an unskilled worker gets Rs.3 a day then a skilled worker gets Rs. 7.50 per day a clerks Rs. 4.50 a day

PARTNERSHIP

When two or more persons start a business jointly and share the profit or loss thereof in an agreed proper portion, it is known as partnership business and the persons carrying on such business are called Partners. Generally partners share the profit or loss in the ratio of the capitals invested by them.
        Partnership may be (1) simple 
                                        (2) compound.
Simple Partnership - When the capitals of the partners are invested for the same time, then this type of partnership is called simple partnership. In such a case, the profit or loss is distributed in proportional to the capital invested.
Compound Partnership - When the capital, which is equal or unequal, of the partners, is invested for different times, this type of partnership is called compound partnership. In such a caste the profit or loss is distributed in proportional to the products of the capital and the periods of their investment.
An important formula for solving the problems of partnership is -
                   
Working Rule -
1. If the ratio of investment by three persons is a: b: c and ratio of time invested in their capital is x: y: z then the ratio of their profit will be ax: by: cz.
2. If the ratio of investment by three persons is a:b:c and ratio of their profit is p:q:r then, the ratio of time invested in their capital will be 
EXAMPLES

Example 1:   A, B and C enter into partnership. A contributes one-third of the capital while B contributes as much as A and C together contribute. If the profit at the end of the year amounts to Rs. 840 what would each receive?
Sol:  As A contributes one-third of the capital 
A’s profit =    = Rs. 280
Now as B contributes as much as A and C
So Profit of B  = Profit of A + Profit of C =  Rs. 280 + Profit of C
Profit of B – Profit of C =  Rs. 280
And   Profit of B + Profit of C =  Rs. 840 – Rs. 280
Adding  2 Profit of B  = Rs. 840
Profit of B  = Rs. 420
Hence   Profit of C  = 840 – 420 - 280
                           = Rs. 140


Example 2:  A is working and B is a sleeping partner in a business. A puts  Rs. 5, 000 and B puts in Rs. 6, 000. A receives 12 ½ % of the profit for Managing  the business and the rest is divided in proportion of their capitals. What does  each get out of a profit of Rs. 880?
Sol: The amount, which A receives for managing
          = 12 ½% of Rs.880
         
         The amount left = 880 – 110 = Rs. 770
         The amount left is to be divided in the ratio = 5,000 : 6,000 = 5: 6
       
         Total share received by A = 110 + 350 = Rs. 460
         Share received by B = Rs. 420


Example 3:  A and B enter into a partnership. A contributes Rs. 5000 while B contributes Rs. 40000. After 1 month B withdraws  1/4 part of his contribution and after 3 months from the starting A puts Rs. 2000 more. When B withdraws his money at the same C also joins them with Rs. 7000. If at the end of 1 year there is a profit of Rs. 1218, what will be share of C in the profit?
Sol:  Since the contributions of three partners are different and their times also differ. Therefore, their contributions should be converted for equal durations. For this, contribution is multiplied by time.
Contribution of A = Rs. 5000 for 12 months + Rs. 2000 for 9 months
Contribution of A for 1 month 
=  5000 × 12 + 2000 × 9
 = 60000 + 18000
= Rs. 78000
Contribution of B = Rs. 4000 for 1 month +   of Rs. 4000 for 11 months
Contribution of B for 1 month
 = 4000 × 1 + 3000 × 11 
= 4000 + 33000 = Rs. 37000
Contribution of C  = Rs. 7000 for 11 months
ontribution of C for 1 month  =  7000 × 11 
= Rs. 77000
Ratio in their contributions  = 78000:37000:77000
                                           = 78:37:77
Sum of their ratios   = 78 + 37 + 77 = 192
Share of C in the profit = 
                                     = Rs. 488.47


Example 4: Alok started a business by investment of Rs.90000 after 3 months Pranav joined him with an investment of Rs. 120000. If they had a profit  of Rs. 96000 after 2 years then what is the difference in the shares of two?
Sol:  Alok’s investment for 1 month  = 9000 × 24 = 2160000
Pranav’s investment for 1 month  = 120000 × 21= 25200
Ratio of their investment   = 6:7

Example 5: A, B and C started a business in partnership. A invested Rs. 25 lacks and after 1 year he invested Rs. 10 lacks more. B invested Rs. 35 lacks in the beginning and withdrew Rs. 10 lacks after 2 years. C invested Rs. 30 lacks. What is the ratio of their profit after 3 years?
Sol:  A’s investment  = 25 × 3 + 10 × 2
                                 = Rs. 95 lacks
B’s investment  = 35 × 2 + 25 × 1
                         = Rs. 95 lacks
C’s investment  = 30 × 3
                         = Rs. 90 lacks
Ratio of their investment  = 19:19:18
Ratio of their profit = 19:19:18 (because time period is same, i.e., for 3 years)


Example 6:  A, B and C investment in a partnership in the ratio of 5:6:8. Ratio of their profit is 5:3:12. Find the ratio of time for their investment.

Example 7:  Three people A, B and C invested money in a partnership in the ratio of 4:2:8 ratio of their time of investment is 3:3:2. What is the ratio of their profit?
Sol:  Required ratio = 4 × 3 : 2 × 3 : 8 × 2
                                    = 12 : 6 :16
                                    =  6 : 3 : 8

NUMBER SYSTEM

    A golden opportunity for Bank exams aspirants. Thousands of posts in SBI and other Banks. Out of five papers in the SBI clerk exam, Quantitative Aptitude plays major role. Arithmetic and Data Interpretation questions will be there in this paper. Arithmetic is the maths, which we use in our day-to-day life. As arithmetic chapters are there upto 10th class only all the aspirants inclusive of non-maths might have studied this. By understanding all the chapters thoroughly and with a lot of practice it is not difficult to solve all the questions of the paper. Also important is simplifications. Out of 40 questions in Q.A., 20 are simplification questions. Students need to mug up tables upto 20, squares of numbers upto 25 and cubes of numbers upto 15 to make simplifications easy. They also learn Speed Maths for solving simplification questions in seconds without pen. All the chapters in arithmetic have to be practiced thoroughly. Let us see all the chapters of arithmetic in detail.
Digit: 0 to 9 are the digits.
Number: By using digits we write numbers.
Face Value: The real value of the digit.
Place Value: The value of the digit according to the place.
e.g.: In 2794, the face value of 7 is '7'and the place value is '700'.
Classification of Numbers:
Odd Numbers
Numbers which are not divisible by 2
e.g.: 1, 3, 5, 7, .......


Even Numbers
Numbers which are divisible by 2
e.g.: 2, 4, 6, 8, .......


Natural Numbers
All counting numbers             e.g.: N = {1, 2, 3, ........}

Whole Numbers
0 and all natural numbers
e.g.: W = { 0, 1, 2, 3, ...}


Integers
Natural numbers, zero and negative of natural numbers
e.g.: I = { ........, -3, -2, -1, 0, +1, +2, +3, .......}


Rational Numbers
These are of the form of p/q, where q π 0
e.g.:  etc


Irrational Numbers
Can't be written in p/q form, where q ≠ 0
e.g.:  π  etc


Composite Numbers
Numbers having more than two factors


Prime Numbers
Numbers divisible by one and the number itself or numbers having only two factors.
e.g.: 2, 3, 5, 7, 11, 13, ...... etc


Some points about prime numbers
All prime numbers end with 1, 3, 7 or 9 except 2 and 5.
* 2 is the only even prime number.
* '1' is neither a prime nor composite number. It is a unitary.
* There are 25 prime numbers upto 100.


Twin prime numbers
The difference between two prime numbers is '2'.
e.g.: 3 - 5, 5 - 7, 11 - 13 etc


Co prime numbers
Numbers not having any common factors.
e.g.: 3, 5 and 8 are co primes to each other.


Some important Identities:
1. (a+b)2 = a2 + b2 + 2ab
2. (a-b)2 = a2 + b2 - 2ab
3. (a+b)(a-b) = a2 - b2
4. (a+b)3 = a3 + b3 + 3a2b + 3ab2
5. (a-b)3 = a3 - b3 - 3a2b + 3ab2
6. a3 + b3 = (a+b)(a2− ab + b2)
7. a3 - b3 = (a− b) (a2 + ab+ b2)
8. (a+b+c)2 = a2+b2+c2 + 2ab + 2bc+2ac
9. a3+b3+c3− 3abc = (a+b+c) (a2 +b2 + c2 - ab -bc-ac)
 
1) 2.01      2) 2       3) 1       4) 1.93        5) None of these
Sol: It is based on the formula a3 + b3 = (a+b)(a2−ab+b2)
1.07 + 0.93 = 2, hence answer (2).
To solve the equations based on numbers, the number is written in algebraic form. 
For example let the number be x.
    The numerator of a fraction is written in the following form
Three-fourth of a number = 
Two-third of a number = 
Double of a number = 2x, Thrice of a number = 3x
20% of a number = 
30% of 3/4 of one-third of a number =  
e.g.: 1.  4/5  of  4/7  of  5/6  of  1218 = ?     (SBI 2008)
(A) 415      (B) 384       (C) 492       (D) 346      (E) None of these
sol:  hence answer (E)
2. One-seventh of a number is 51. What will be 64% of that number?       (SBI 2008)
    (A) 248.12     (B) 228.48      (C) 238.24      (D) 198.36     (E) None of these
Sol:
 

 hence answer (E)

3. If (16)3 is subtracted from the square of a number, the answer so obtained is 3825. What is the number ?      (SBI 2008)
(A) 69     (B) 59     (C) 89      (D) 79    (E) None of these
Sol: Let the number be x  
x2− 163= 3825  x = 89
 hence answer (C).
4. If (92)2 is added to the square of a number, the answer so obtained is 10768. What is the number?          (SBI 2008)
(A) 46         (B) 2304        (C) 48        (D) 2116       (E) None of these
Sol: Let the number be x
x2+ 922= 3825  x = 48
hence answer (C).
5. If an amount of Rs. 97,836 is distributed equally amongst 31 children. How much amount would each child get?    (SBI 2008)
(A) Rs.3,756    (B) Rs.3,556    (C) Rs. 3,356    (D) Rs. 3,156    (E) None of these 
Sol:     hence answer (D).
     Three consecutive odd numbers are x, (x+2) and (x+4), or (x-2), x and (x+2), where x is an odd number.
     Similarly, three consecutive even numbers are x, (x+2) and (x+4) or (x-2), x and (x+2) where x is an even number
     If a number 'a' is multiplied by itself for n times, the product is called n th power of
'a'. This is written as an.
     In an, a is called base and n is called index or exponent or power.
All simplification questions have to be solved based on BODMAS rule only.
  B - Bracket
  O - Of
  D - Division
  M - Multiplication
  A - Addition
  S - Subtraction
e.g. 1: What is 394 times 113? (SBI 2008)
(A) 44402       (B) 44632       (C) 44802      (D) 44522     (E) None of these
Sol:   394 × 113 = 44522,     hence answer (D)
2. What approximate value should come in place of the question mark (?) in the following question?  4780 ÷ 296 × (23)2 = ?
(A) 9870      (B) 6760      (C)7590     (D) 3430      (E) 8540
Sol: × 529 = 8542.63
Approximately 8540, hence answer(E)
3. When 40% of first number is added to the second number the second number becomes 1.2 times of itself. What is the ratio between the first and second numbers?
(A) 2:3      (B) 4:3       (C) 1:2      (D) 5:7      (E) None of these
Sol: Let the first and second number be x and y

Grammar Rules

If you observe the previous question papers you can conclude that Grammar is tested through the following question types:
     * Sentence Completion. (Fill in the blanks)
     * Sentence Correction. (Spotting errors)
     * Sentence Fillers.
     * Sentence Improvement.
All the areas mentioned above deal with only one point that is accuracy in using English. If one knows a few Grammar rules, whatever be the question type, one can solve the questions easily. Those Grammar rules cover: Nouns, Pronouns, Verb and tense, Modifiers
(Adjectives and Adverbs), Prepositions, Conjunctions, Articles, Concord (Subject and verb agreement), Parallelism...
       Before going any further, lets pay a glance at how a single grammar rule can be asked in above mentioned varieties.

Let's take up sentence completion.
1. We did the job ........... we could; however, it did not turnout to be satisfactory.
    A) Better          B) as good as             C) as better as            D) as well as          E) worse.
     The same question can be asked as a sentence correction, what we call, spotting
error
.
2. We did the job (A)/as good as (B) /we could, however, it did not (C)/ turn out to be satisfactory (D)/ No error(E).
     Let's have a look at the same question as a sentence filler.

3. The job did not turn out to be satisfactory, though we did it ..............
    A) as good as we could
    B) as well as we could
    C) better we could
    D) as better as we could
    E) worse we could
Let's observe the same question in the remaining variety- sentence improvement. In this
question type the sentence, a part of the sentence is underlined and asked whether it needs
any improvement. Finally, after the instructions the question looks like this:

4. We did the job as good as we could; however, it did not turnout to be satisfactory.
    A) as better as we could
    B) as well as we could
    C) as worse as we could
    D) better we could
    E) No improvement
    Whatever may be the question type the grammar rule tested in the above questions is
the same one. If you know the usage as given below, it is easy to answer the above ones.
Usages: It is an adverb that we use to describe an action. Here, in this sentence, the verb did is described and used as a positive degree. It is very clear if you observe as x as. The proper forms are:

Positive            Comparative           Superlative 

good                 better                      best 

well                  better                       best 

ill                      worse                     worst  

bad                 worse                        worst   

       If you observe comparative and superlative, you can see the same word as comparative for both good and well. Like wise, the same word as superlative for those two words. But, infact 'good' is an adjective and used to describe a noun whereas 'well' is an adverb and used to describe a verb.
       In the given question it is an adverb that we need so 'as well as' goes with the sentence as a proper answer. 
       Finally, if you know the usage of adjective and adverb including their degrees, you candeal with the question without any hesitation.
Therefore, the answers are:    1. D,        2. B,        3. B,        4. B.
       In conclusion, we can say that, one should know a few grammar rules that frequently
appear on the tests so that one can succeed.
Let's turn to those grammar rules:
       As mentioned above, Grammar rules related to nouns, pronouns, verb and tense etc... are tested most frequently. So lets tearup one by one.

Nouns: This 'Nouns' area has been tested on umpteen number of tests. The basic problems in Noun usage are:
       A) Noun and its form
       B) Noun and number
       C) Noun and article
       D) Noun and verb agreement
       E) Noun and pronoun agreement

How to crack these areas:
If you have a good command of the following words, it will be a cake walk for you.
       * A few nouns are always singular
       * A few nouns are always plural
       * A few nouns look like singular but plural in their usage
       * A few nouns look like plural but singular in fact
       * Some nouns are used both as singulars and plurals without changing their form (Structure).

A few Nouns which are always singular.
       * The below given nouns do not give plural meaning.
       * They do not become plurals even by changing their form.
       * They do not take plural verbs after them.
       * They do not take plural pronouns.
Examples: Scenery, advice, information, machinery, stationery, furniture, rice, gram, repair, poetry, business, luggage, mischief, bread, land, hair, issue.
How do questions appear on these words:
e.g.1:
 I have sold all my furnitures which have become waste.
Ans: I have sold all my furniture which has become waste.
e.g.2: Her hairs indicate that she has become old.
Ans: Her hair indicates that she has become old.
A few Nouns which are always plural.
       * These nouns do not get singular form.
       * These do not take singular verb after them.
       * These do not take singular pronoun.
Examples: Trousers, scissors, spectacles, ashes, goods, thanks, annals, tidings, shorts,
alms, proceeds, remains, riches, tongs, pantaloons, credentials, premises.

Example questions:
e.g.1: Where is my trouser?
Ans: Where are my trousers?
e.g. 2: The proceeds of the magic show is to be given to the fund for the soldiers' welfare.
Ans: The proceeds of the magic show are to be given to the fund for the soldiers' welfare. A few Nouns look like singular but plural in their usage:
Examples: Cattle, gentry, vermin, peasantry, people, artillery, clergy, company, police, poultry, swine.
Example questions:
e.g.1: The latest poultry is ready for sale.
Ans: The latest poultry are ready for sale.
e.g.2: All the gentries are invited to the party.
Ans: All the gentry are invited to the party.
A few Nouns looks like plural but singular in meanings:
Examples: Innings, athletics, economics, mathematics, summons, gallows, gymnastics,
wages, news, physics, dynamics, civics, linguistics, tactics, politics, electronics.

Example questions:
e.g. 1. Through the electronic media the news are travelling faster than ever before.
Ans: Through the electronic media the news is travelling faster than ever before.
e.g. 2. The police have been unable to serve a summon on the minister.
Ans: The police have been unable to serve a summons on the minister.
A few Nouns which function both as singu and plurals without changing their form (structure).
Examples: Sheep, Species, deer, aircraft, offspring, space craft, salmon, yoke.

Example questions:
e.g. 1. sheeps live in flocks
Ans: sheep live in flocks
e.g. 2: I saw four deers in the zoo.
Ans: I saw four deer in the zoo. Besides the above mentioned, the following areas have been tested in many an examinations. Let's learn these error prone areas through the question pattern itself.

1. She gave me a cheque for five thousands rupees.
Ans: She gave me a cheque for five thousand rupees.

2. Last month I attended a two-weeks programme on personality development
Ans: Last month I attended a two-week programme on personality development.
Note: Some nouns which indicate a specific amount, length, weight, quantity, measure, or
number etc... remain unchanged in form especially when they are preceded by a numeral. (Those nouns include - foot, metre, score, dozen, year, hundred, thousand, million, week, pair, month, KM, Kg etc ...)

3: This was one of the reason why the industry flourished.
Ans: This was one of the reasons why the industry flourished.

4: He got demotion and one of the reasons are his carelessness.
Ans: He got demotion and one of the reasons is his carelessness.
Note: 1) 'One of' always takes a plural noun after it.
            2) 'One of + Plural noun' takes only singular verb.

5: The number of orders still to be executed are growing up day by day.
Ans: The number of orders still to be executed is growing up day by day.

6: A number of students is absent from the class today.
Ans: A number of students are absent from the class today.
Note: 'The number of' is considered singular and 'A number of' is treated plural. So the verb needs to be used accordingly.

7: Today, I have got many works to do.
Ans: Today, I have got much work to do (or) Today I have got many tasks to do.
Note: 'WORK' is always in singular as a noun.

8: Two-thirds of the mailing list have been typed.
Ans: Two-thirds of the mailings list has been typed.
9: Two-thirds of our employees lives in the suburbs.
Ans: Two-thirds of our employees live in the suburbs.
Note: After such expressions as-One-half of, two-thirds of, a part of, a majority
of, - we use singular verb it the noun is singular and a plural verb if the noun is plural.

10: Rupa and Prabha are my family members.
Ans: Rupa and Prabha are the members of my family.

11: Pranava and Manya are the Parliament Members.
Ans: Pranava and Manya are the members of the Parliament.
Note: 'Member of Something' is the proper expression.

12: Uma is my cousin sister.
Ans: Uma is my cousin.
Note: Cousin is enough in the place of cousin brother or cousin sister.

13: He has four sister-in-laws.
Ans: He has four sisters-in-law
Note: The proper expressions as plurals are: Sisters-in-law, brothers-in-law, commanders-inchief, men-servant, step mothers, arm chairs, advocates general, passers by, officers-incharge (i.e. only head words become plurals)

PARTNERSHIP

When two or more persons start a business jointly and share the profit or loss thereof in an agreed proper portion, it is known as partnership business and the persons carrying on such business are called Partners. Generally partners share the profit or loss in the ratio of the capitals invested by them.
        Partnership may be (1) simple 
                                        (2) compound.
Simple Partnership - When the capitals of the partners are invested for the same time, then this type of partnership is called simple partnership. In such a case, the profit or loss is distributed in proportional to the capital invested.
Compound Partnership - When the capital, which is equal or unequal, of the partners, is invested for different times, this type of partnership is called compound partnership. In such a caste the profit or loss is distributed in proportional to the products of the capital and the periods of their investment.
An important formula for solving the problems of partnership is -
                   
Working Rule -
1. If the ratio of investment by three persons is a: b: c and ratio of time invested in their capital is x: y: z then the ratio of their profit will be ax: by: cz.
2. If the ratio of investment by three persons is a:b:c and ratio of their profit is p:q:r then, the ratio of time invested in their capital will be 
EXAMPLES

Example 1:   A, B and C enter into partnership. A contributes one-third of the capital while B contributes as much as A and C together contribute. If the profit at the end of the year amounts to Rs. 840 what would each receive?
Sol:  As A contributes one-third of the capital 
A’s profit =    = Rs. 280
Now as B contributes as much as A and C
So Profit of B  = Profit of A + Profit of C =  Rs. 280 + Profit of C
Profit of B – Profit of C =  Rs. 280
And   Profit of B + Profit of C =  Rs. 840 – Rs. 280
Adding  2 Profit of B  = Rs. 840
Profit of B  = Rs. 420
Hence   Profit of C  = 840 – 420 - 280
                           = Rs. 140


Example 2:  A is working and B is a sleeping partner in a business. A puts  Rs. 5, 000 and B puts in Rs. 6, 000. A receives 12 ½ % of the profit for Managing  the business and the rest is divided in proportion of their capitals. What does  each get out of a profit of Rs. 880?
Sol: The amount, which A receives for managing
          = 12 ½% of Rs.880
         
         The amount left = 880 – 110 = Rs. 770
         The amount left is to be divided in the ratio = 5,000 : 6,000 = 5: 6
       
         Total share received by A = 110 + 350 = Rs. 460
         Share received by B = Rs. 420


Example 3:  A and B enter into a partnership. A contributes Rs. 5000 while B contributes Rs. 40000. After 1 month B withdraws  1/4 part of his contribution and after 3 months from the starting A puts Rs. 2000 more. When B withdraws his money at the same C also joins them with Rs. 7000. If at the end of 1 year there is a profit of Rs. 1218, what will be share of C in the profit?
Sol:  Since the contributions of three partners are different and their times also differ. Therefore, their contributions should be converted for equal durations. For this, contribution is multiplied by time.
Contribution of A = Rs. 5000 for 12 months + Rs. 2000 for 9 months
Contribution of A for 1 month 
=  5000 × 12 + 2000 × 9
 = 60000 + 18000
= Rs. 78000
Contribution of B = Rs. 4000 for 1 month +   of Rs. 4000 for 11 months
Contribution of B for 1 month
 = 4000 × 1 + 3000 × 11 
= 4000 + 33000 = Rs. 37000
Contribution of C  = Rs. 7000 for 11 months
ontribution of C for 1 month  =  7000 × 11 
= Rs. 77000
Ratio in their contributions  = 78000:37000:77000
                                           = 78:37:77
Sum of their ratios   = 78 + 37 + 77 = 192
Share of C in the profit = 
                                     = Rs. 488.47


Example 4: Alok started a business by investment of Rs.90000 after 3 months Pranav joined him with an investment of Rs. 120000. If they had a profit  of Rs. 96000 after 2 years then what is the difference in the shares of two?
Sol:  Alok’s investment for 1 month  = 9000 × 24 = 2160000
Pranav’s investment for 1 month  = 120000 × 21= 25200
Ratio of their investment   = 6:7

Example 5: A, B and C started a business in partnership. A invested Rs. 25 lacks and after 1 year he invested Rs. 10 lacks more. B invested Rs. 35 lacks in the beginning and withdrew Rs. 10 lacks after 2 years. C invested Rs. 30 lacks. What is the ratio of their profit after 3 years?
Sol:  A’s investment  = 25 × 3 + 10 × 2
                                 = Rs. 95 lacks
B’s investment  = 35 × 2 + 25 × 1
                         = Rs. 95 lacks
C’s investment  = 30 × 3
                         = Rs. 90 lacks
Ratio of their investment  = 19:19:18
Ratio of their profit = 19:19:18 (because time period is same, i.e., for 3 years)


Example 6:  A, B and C investment in a partnership in the ratio of 5:6:8. Ratio of their profit is 5:3:12. Find the ratio of time for their investment.

Example 7:  Three people A, B and C invested money in a partnership in the ratio of 4:2:8 ratio of their time of investment is 3:3:2. What is the ratio of their profit?
Sol:  Required ratio = 4 × 3 : 2 × 3 : 8 × 2
                                    = 12 : 6 :16
                                    =  6 : 3 : 8

Time & Work

Work is always taken as one unit. Construction of a building, filling water in the tank, painting a room etc.

To complete a job, a man will do the same amount of work on each day of the total number of days he takes to complete that job.
If a man can do a piece of work in 8 days, then his one day’s work is  .
If a man’s one day’s work is  then he can complete the total work in 4 days.
If a man can complete a piece of work in A days and another man can complete the  same work in B days,
then they together can complete the work in   days.
Similarly, three persons A, B and C together can complete in   days.
Ex: A can complete a piece of work in 6 days and B in 8 days. In what time they complete if they work together?


MAN DAYS: 
If 6 men can complete a work in 4 days, then the number of man days required to complete that work is 6 × 4 = 24.
Whatever may be the number of persons working on that, the total number of man days required for that work will be 24.
Ex:18 men together can complete a work in 14 days. In how many days 12 men finish that work?
A) 5 dyas       B) 6 days     C) 10 days       D) 8 days      E) None of these

Men and Time are inversely proportional i.e., when more men work, they take less time to complete the work. Similarly when less men work, they take more time to complete the work.
       Men and Work are directly proportional i.e., when more men are there, they do more work and less men are there, they do less work.
Similarly, Time and Work are also directly proportional. If men work for more time then they do more work and less time then the work is also less.
The relation among these variables can be shown in a formula
If M is Men, D is Days (Time) and W is work then 

Ex:  A contractor employs 12 men to complete a work in 15 days. But after 8days he notices that only 30% work has been completed. In order to finish the work in the given time, how many more men he has to recruit?
A) 32         B) 24         C) 20       D) 9         E) None of these


To complete the remaining work 32 men are required
Additional men required 32 - 12 = 20
Hence answer is (c)


PIPES AND CISTERNS
       The problems in pipes and cisterns are almost the same as those of Time and Work problems.
Ex: If a pipe fills a cistern in 12 hours and a leak in the bottom empties it in15 hours. In what time can the tank be filled when both function simultaneously?
Sol:    Pipe’s one hour’s work  =  
           Leak’s one hour’s work  =   (negative work)
           Pipe and leak together can do   work in one hour.
           Net work is Positive.
           Tank will be filled in 60 hours.


Some more models:
1. A can complete a piece of work in 240 days. A and B together can complete the same work in 144 days. In what time does B alone complete that work?
A) 15 days      B) 96 days         C) 148 days       D) 360 days         E) 240 days


2. A can do a piece of work in 12 days. B is 60% more efficient than A. In how many days B alone finish the work?


3. 14 men can do a piece of work in 12 days. 5 days after they started the work, 6 more men joined them. How many days will they now take to complete the remaining work?
A) 10 days      B) 12 days      C) 14 days     D) 8 days     E) None of these


4.   A can do a piece of work in 20 days. B can do the same work in12days. If B worked on the work for 9 days, how many days A worked on it?


5. Two pipes A and B can fill a tank in 3 and 4 hours respectively. A drain pipe C can empty a full tank in 6 hours. In what time can the tank be filled when all the three are open simultaneously?
A) 7.5 hours     B) 2.4 hours    C) 1 hours    D) 6 hours     E) None of these
Sol: A = 3 (+) , B = 4 (+) , C = 6(-)

 Tenses  

                పోటీ పరీక్షలో విజయాన్ని నిర్దేశించే General English లో ఎక్కువ మార్కుల కోసం గ్రామర్‌లో అతి కీలకమైన tenses మీద పట్టు సాధించడం అవసరం. tenses ను Heart of English Grammar గా అభివర్ణిస్తారు. ఆంగ్లంలో మాట్లాడాలన్నా, రాయాలన్నా, ఆ భాషపై భయం తొలగిపోవాలన్నా 'tenses' మీద పట్టు సాధించడం అనివార్యం. అంతేకాకుండా ఇంగ్లిష్ గ్రామర్‌లో voice, speech లాంటి ఇతర అంశాలు కూడా పరోక్షంగా tenses మీద ఆధారపడి ఉంటాయి. కాబట్టి, మనం tenses ని ఎంత చక్కగా అర్థం చేసుకోగలిగితే, మిగతా విభాగాలనూ అంతే బాగా అర్థం చేసుకోగలం.
Tenses అనే పదం 'tempus' అనే లాటిన్ పదం నుంచి పుట్టింది. లాటిన్‌లో'tempus' అంటే 'time' అని అర్థం. 'tense'అనేది పని జరిగే కాలాన్ని సూచిస్తుంది.

 Tense = Time + Action
ఇంగ్లిష్‌లో ప్రధానంగా మూడు Tenses ఉన్నాయి.
అవి:     
      1. Present tense 
      2. Past tense
      3. Future tense.
 ప్రతి tenseకి నాలుగు Sub tenses (ఉప కాలాలు) ఉంటాయి.
అవి:
      1. Simple
      2. Continuous
      3. Perfect
      4. Perfect Continuous.
ఇలా.. ఇంగ్లిష్‌లో మొత్తం tenses: 3 × 4 =12.

మనం ఇప్పుడు ఈ12 tenses గురించి నేర్చుకోవాలి. ఇక్కడ ప్రతి tense కి సంబంధించి ముఖ్యంగా 3 అంశాలు నేర్చుకోవాలి. అవి:
1. Structure (నిర్మాణం)
2. Usage (ఉపయోగం)
ముందుగా structureకు సంబంధించి ఒక ముఖ్యమైన అంశాన్ని మనం ఇక్కడ గ్రహించాలి. అదే వాక్య నిర్మాణం. ఇంగ్లిష్‌కు, మిగతా భాషలకు వాక్య నిర్మాణంలో చాలా తేడా ఉంది. కింది వాక్యాన్ని గమనించండి.
                        సీత         యాపిల్         తిన్నది.   
                        కర్త             కర్మ              క్రియ 
                        Subject     Object         Verb
ఈ వాక్యాన్ని ఇదే క్రమంలో English లోకి అనువదిస్తే ఆ వాక్యం ఇలా ఉంటుంది.
                        Sita     an apple     ate
కానీ, ఈ వాక్యం తప్పు కదా! sita ate an apple అని ఉండాలి.
                          కర్త                 క్రియ          కర్మ
                        Subject         Verb        Object
దీని నుంచి మనం గ్రహించేది ఏమిటంటే:
ఇంగ్లిష్‌లో వాక్య నిర్మాణం S + V + O
మిగతా భాషల్లో వాక్యనిర్మాణం S + O + V
ఈ 12టెన్స్‌ల నిర్మాణాలు, ఉపయోగాలు, ఆ tense ను గుర్తించడానికి అవసరమయ్యే clue words ని పట్టిక రూపంలో చూడొచ్చు. వీటిని క్షుణ్నంగా నేర్చుకుంటే tenses పై అడిగే ప్రశ్నలకు సమాధానాలు సులభంగా గుర్తించవచ్చు.
(తరువాత పేజీలోని పట్టిక చూడండి.)




పరీక్షలో tenses పై అడిగే ప్రశ్నలకు సమాధానాలు గుర్తించే పద్ధతి:
మొదటి దశ: ఇచ్చిన వాక్యాన్ని జాగ్రత్తగా చదివి, అర్థం చేసుకొని, ఏ tense కు చెందిందో నిర్ధారించుకోవాలి.
రెండో దశ: Clue word ను గుర్తించి, తద్వారా ఇచ్చిన వాక్యం కచ్చితంగా ఏ tense కు (నాలుగు sub tenses లో) చెందిందో గుర్తించాలి.
మూడో దశ: కచ్చితమైన tense ని నిర్ధారించిన తరువాత ఆ tense structure ను గుర్తుకు తెచ్చుకొని, కింద ఇచ్చిన నాలుగు ప్రత్యామ్నాయాల్లో ఏది సరిపోతుందో చూసి, సమాధానాన్ని గుర్తించాలి.

 

Illustrative Examples:
1. While he ---- the road, he met with an accident.

     1) is crossing            2) was crossing
     3) cross                    4) will be crossing
I st method: ఇచ్చిన వాక్యాన్ని చదివిన వెంటనే ఆ వాక్యం Past tense కు చెందిందిగా గుర్తించవచ్చు. ఎందుకంటే met అనేVerb Past Tense (V2)ను సూచిస్తుంది. ఇచ్చిన వాక్యం అర్థాన్ని గ్రహించడానికి ప్రయత్నించినప్పుడు 'అతడు రోడ్డు దాటుతూ ఉండగా అతడికి ప్రమాదం జరిగింది' అనే అర్థాన్ని స్ఫురింపజేస్తుంది. అంటే, గతంలో జరుగుతూ ఉండిన పని(Past Continuous Tense) అని తెలుస్తుంది. ఆ Tenseనిర్మాణం మనకు తెలుసు కాబట్టి 2వ ఆప్షన్‌ను సమాధానంగా గుర్తించవచ్చు.

 

II nd Method: V2 + While అనేClue words Past Continuous Tense ను సూచిస్తాయి. కాబట్టి 1, 3వ ప్రత్యామ్నాయాలు సమాధానాలు కావు. ఎందుకంటే ఆ రెండు Present Tense ను సూచిస్తాయి. 4 కూడా సరైన సమాధానం కాదు. ఎందుకంటే అది Future Tense ను సూచిస్తుంది. కాబట్టి '2' మాత్రమే సరైన సమాధానం.
 

2. It ----- heavily since morning.
1) is raining              2) was raining             3) has been raining              4) rained
Ans: ఇచ్చిన వాక్యంలో since అనేది Clue word since/ for present perfect continuous tense ను సూచిస్తుంది కాబట్టి, సమాధానం 3 అని సులభంగా గుర్తించవచ్చు.

 

3. The patient ---- before the doctor arrived. 
   1) died              2) die                   3) has died                4) had died
Ans: ఇచ్చిన వాక్యంలో arrived (V2) ఉంది కాబట్టి, చూసిన వెంటనే Past tense అని గుర్తించవచ్చు. V2 + before/ after/ when Past Perfect Tense ను సూచిస్తుంది కాబట్టి సమాధానాన్ని 4 గా గుర్తించవచ్చు.

 

4. At present he ---- in Tirupathi.
   1) lives              2) is living             3) was living              4) lived
Ans: At Present అనేదిPresent Continuous Tense ను సూచిస్తుంది కాబట్టి, సమాధానం 2.

 

5. Birds ---- every year.
1) migrate              2) migrated             3) are migrating              4) migrates
Ans: Every అనేది Simple Present Tense ని సూచిస్తుంది కాబట్టి సమాధానం '1'.  

Antonyms

           An ‘antonym’ is often defined as a “word that is contrary in meaning to another”. It is nothing but a word opposite in meaning to the given word. It so happens sometimes that we need to supply an antonym to the given word based on the context in which it is used. As such, anantonym can be opposite in – meaning, gender, status, location, degree, nature and so forth. So,to pick up an antonym to the given word, we need to be provided with the information in which the given word is placed and is in the requirement of its opposite.
           Antonyms form an integral part of the English Language. Acquaintance with the vocabulary of the English language is a necessity for effective expression either in the written or in the oral from. Antonyms are the negative connotation of a particular word. So, it is a word or phrase that is opposite in meaning to a particular word or a phrase in the same language.
           We must remember the following hints to be quite alert while choosing an antonym to thegiven word.
*   We should bear in mind that an antonym must be in the same part of speech in which the given word is.
*    We should note that the answer should be in the same tense form in which the given word is.
*  We must pay due attention to the fact that generally the question paper setters include a synonym in the alternative choices, given for the answer of the key word.
* Often the alternative answers are in Active as well as in Passive Voice. The correct answer is that which is similar in voice to the key word.
            An antonym is a word opposite in meaning to another word but similar to it in most other respects. For example, tall and short are opposite in meaning but both are the same parts of speech (adjectives) and would take the same position in a sentence (before the noun they modify).
            Antonyms tend to be adjectives, adverbs and verbs, with relatively few nouns qualifying as true antonyms. For example high (an adjective), slowly (an adverb) and “to fast” (a verb) all have antonyms, while “table” (a noun) does not.
            It is meant to help to improve the vocabulary of the visitors, the students (who are preparing for various examinations), the authors, journalists, literati and all other people who are interested in improving their language skills.
Requirement of appropriate word for the appropriate occasion is inevitable because only with a good knowledge of words one can express the thoughts and feelings meticulously.

 

COMMIT TO MEMORY
Antonyms can be formed in three ways:

1. By adding a prefix like – un, non, dis, mis, anti, de, il, im, in, ir, mal
2. By adding a suffix like – less, ful,
3. By using a new word.
Eg:
              Word                                 Antonym
               haramful             -          harmless
                hasten                 -          dawdle
                healthy                -          unhealthy
                hill                       -           valley
                honest                 -          dishonest
                humble               -           proud
                inhabited            -           uninhabited
                intelligent           -           un intellijent, stupid.
                interesting          -           un interesting
                lawful                  -            un lawful
                like                       -             dislike
                understand          -             misunderstand
                miser                   -             spendthrift
                mature                 -              immature
                optimist               -              pessimist
                peace                   -               war
                loud                     -               soft 
                plentiful               -               scarce
                possible              -               impossible

Antonyms

           An ‘antonym’ is often defined as a “word that is contrary in meaning to another”. It is nothing but a word opposite in meaning to the given word. It so happens sometimes that we need to supply an antonym to the given word based on the context in which it is used. As such, anantonym can be opposite in – meaning, gender, status, location, degree, nature and so forth. So,to pick up an antonym to the given word, we need to be provided with the information in which the given word is placed and is in the requirement of its opposite.
           Antonyms form an integral part of the English Language. Acquaintance with the vocabulary of the English language is a necessity for effective expression either in the written or in the oral from. Antonyms are the negative connotation of a particular word. So, it is a word or phrase that is opposite in meaning to a particular word or a phrase in the same language.
           We must remember the following hints to be quite alert while choosing an antonym to thegiven word.
*   We should bear in mind that an antonym must be in the same part of speech in which the given word is.
*    We should note that the answer should be in the same tense form in which the given word is.
*  We must pay due attention to the fact that generally the question paper setters include a synonym in the alternative choices, given for the answer of the key word.
* Often the alternative answers are in Active as well as in Passive Voice. The correct answer is that which is similar in voice to the key word.
            An antonym is a word opposite in meaning to another word but similar to it in most other respects. For example, tall and short are opposite in meaning but both are the same parts of speech (adjectives) and would take the same position in a sentence (before the noun they modify).
            Antonyms tend to be adjectives, adverbs and verbs, with relatively few nouns qualifying as true antonyms. For example high (an adjective), slowly (an adverb) and “to fast” (a verb) all have antonyms, while “table” (a noun) does not.
            It is meant to help to improve the vocabulary of the visitors, the students (who are preparing for various examinations), the authors, journalists, literati and all other people who are interested in improving their language skills.
Requirement of appropriate word for the appropriate occasion is inevitable because only with a good knowledge of words one can express the thoughts and feelings meticulously.

 

COMMIT TO MEMORY
Antonyms can be formed in three ways:

1. By adding a prefix like – un, non, dis, mis, anti, de, il, im, in, ir, mal
2. By adding a suffix like – less, ful,
3. By using a new word.
Eg:
              Word                                 Antonym
               haramful             -          harmless
                hasten                 -          dawdle
                healthy                -          unhealthy
                hill                       -           valley
                honest                 -          dishonest
                humble               -           proud
                inhabited            -           uninhabited
                intelligent           -           un intellijent, stupid.
                interesting          -           un interesting
                lawful                  -            un lawful
                like                       -             dislike
                understand          -             misunderstand
                miser                   -             spendthrift
                mature                 -              immature
                optimist               -              pessimist
                peace                   -               war
                loud                     -               soft 
                plentiful               -               scarce
                possible              -               impossible

Synonyms

          Synonyms are the words that are similar or nearly similar in meaning. A synonym, thus, has a literal meaning while its implied meaning may be different. Defining a synonym, the Concise Oxford Dictionary of Current English mentions – A synonym is a “word or phrase identical and coextensive in sense and usage with another of the same language”. Oxford Advanced Learners Dictionary of Current English writes – A synonym is a “word denoting the same thing as another but suitable to different emphasis”.
          As such, a synonym is a word or expression accepted as a figurative or symbolic substitute for another word or expression. In other words, we can say that a synonym is a word which has the same or almost the same meaning as that of another word in the same language.
          It may, however, be noted that, except in rare cases, no two words are exact synonyms that are interchangeable in all the contexts in which either might appear. However, within a given context, there are often close synonyms. For example: teach, educate and instruct convey more or less same meanings and can be called synonyms though they slightly differ from one another, principally in degrees of abstraction.
Hence words which are synonymous in one of their meanings may differ considerably in their other meanings.
 

COMMIT TO MEMORY
There are certain points which we should remember while choosing a synonym.
They are:
* A synonym should be in the same Part of Speech in which the given word is.
* A synonym, as mentioned above, may have a literal meaning and another an implied meaning. So, we should not choose a synonym blindly but be careful whether we have chosen the right word on the basis of the information given in the context.
* Sometimes, the examiners include an antonym in the alternative choices given for the answer of that synonym. Hence, we must be very cautious in choosing a synonym.
 

MIND MAP OF CHOOSING A SYNONYM
         We come to know the brain storming scene of choosing a synonym if we observe the following mind map. The word ‘question’ is the entry for choosing a synonym in the context. The detailed explanation in regard to the selection of the right synonym in the context is offered there under the mind map.

 

CASE 1:

Main Entry     : question
Part of Speech: noun
Definition       : issue, point at issue
Synonyms       : discussion, motion, point, problem, proposal, proposition, subject, theme, topic
Antonyms       : agreement
 

CASE 2:

Main Entry      : question
Part of Speech :verb
Definition        :  ask for answer
Synonyms        : ask about, catechize, challenge, cross-examine, enquire, examine, give the third degree, go over, grill, hit up, hit*, hold out for, inquire, interrogate, interview, investigate, knock*, make inquiry, petition, pick one's brains, probe, pry, pump, put through the wringer, put to the question, query, quest, quiz, raise question, roast, search, seek, show curiosity, solicit, sound out, sweat it out of, work over
Antonyms         : answer, reply                           ( Note: * = informal/non-formal usage)
 

CASE 3:

Main Entry       : question
Part of Speech  : verb
Definition         : doubt
Synonyms         : call into question, cast doubt upon, challenge, controvert, disbelieve, dispute, distrust, hesitate, impeach, impugn, mistrust, oppose, puzzle over, query, suspect, suspicion, wonder about
Antonyms         : certainty, doubtlessness, sureness, surety
 

FORMATS OF QUESTIONS ON SYNONYMS

FORMAT 1:
* Choose the word/group of words which is most nearly the SAME in meaning as the word/group of words given in bold as used in the passage. (In this case, a word for choosing the synonym is taken from the passage meant for Reading Comprehension.)

e.g. tore out
           1. came out gently
           2. pushed out
           3. walked out
           4. rushed out forcefully
           5. destroyed angrily
Ans.  tore out : (4) rushed out forcefully
 

FORMAT 2:
* In each of the following questions, out of the given alternatives, choose the one which best expresses the meaning of the given word.
 

e.g. ABNEGATION
             a. self-denial
             b. self-sacrifice
             c. self-praise
             d. self-criticism
Ans. ABNEGATION: (a) self-denial
 

FORMAT 3:
* In each of the following questions, there are three words which are meanings of a certain
word. Select that word from the answer choices provided in each question.
 

e.g. everlasting, endless, unending
             (a) living
            (b) eternal
            (c) increased
            (d) durable
Ans. everlasting, endless, unending: (b) eternal
 

FORMAT 4
* In each of the following questions, there are four words marked a-d. While three of them are synonymous or have more or less same meaning, one is altogether different from the rest. Select from the answer choices the word which is different from the rest.
 e.g.  (a) witty   (b) pleasant (c) comical (d) humorous                                   
Ans. (b) pleasant
 

FORMAT 5
* In each of the following questions, four pairs of words are given, marked a-d. Each pair consists of two words which have more or less similar meaning. However, one pair consists of two words which are different in meaning, which you have to select as your answer.
 e.g.  (a) authentic/genuine (b) genius/aptitude (c) ghastly/crime (d) gruesome/grim
Ans.  (c) ghastly/crime
 

FORMAT 6
* In each of the following questions, a sentence is given in which one word is printed in bold type. Under each sentence four alternatives, marked a-d are given. Your task is to select the word or expression from the alternatives which convey more or less same meaning as the word printed in bold type.
e.g. The U.N. coalition forces immediately went into action. (a) most powerful (b) faithful (c) temporary alliance (d) selective
Ans.  (c) temporary alliance

Synonyms

          Synonyms are the words that are similar or nearly similar in meaning. A synonym, thus, has a literal meaning while its implied meaning may be different. Defining a synonym, the Concise Oxford Dictionary of Current English mentions – A synonym is a “word or phrase identical and coextensive in sense and usage with another of the same language”. Oxford Advanced Learners Dictionary of Current English writes – A synonym is a “word denoting the same thing as another but suitable to different emphasis”.
          As such, a synonym is a word or expression accepted as a figurative or symbolic substitute for another word or expression. In other words, we can say that a synonym is a word which has the same or almost the same meaning as that of another word in the same language.
          It may, however, be noted that, except in rare cases, no two words are exact synonyms that are interchangeable in all the contexts in which either might appear. However, within a given context, there are often close synonyms. For example: teach, educate and instruct convey more or less same meanings and can be called synonyms though they slightly differ from one another, principally in degrees of abstraction.
Hence words which are synonymous in one of their meanings may differ considerably in their other meanings.

 

COMMIT TO MEMORY
There are certain points which we should remember while choosing a synonym.
They are:
* A synonym should be in the same Part of Speech in which the given word is.
* A synonym, as mentioned above, may have a literal meaning and another an implied meaning. So, we should not choose a synonym blindly but be careful whether we have chosen the right word on the basis of the information given in the context.
* Sometimes, the examiners include an antonym in the alternative choices given for the answer of that synonym. Hence, we must be very cautious in choosing a synonym.

 

MIND MAP OF CHOOSING A SYNONYM
         We come to know the brain storming scene of choosing a synonym if we observe the following mind map. The word ‘question’ is the entry for choosing a synonym in the context. The detailed explanation in regard to the selection of the right synonym in the context is offered there under the mind map.

 

CASE 1:

Main Entry     : question
Part of Speech: noun
Definition       : issue, point at issue
Synonyms       : discussion, motion, point, problem, proposal, proposition, subject, theme, topic
Antonyms       : agreement

 

CASE 2:

Main Entry      : question
Part of Speech :verb
Definition        :  ask for answer
Synonyms        : ask about, catechize, challenge, cross-examine, enquire, examine, give the third degree, go over, grill, hit up, hit*, hold out for, inquire, interrogate, interview, investigate, knock*, make inquiry, petition, pick one's brains, probe, pry, pump, put through the wringer, put to the question, query, quest, quiz, raise question, roast, search, seek, show curiosity, solicit, sound out, sweat it out of, work over
Antonyms         : answer, reply                           ( Note: * = informal/non-formal usage)

 

CASE 3:

Main Entry       : question
Part of Speech  : verb
Definition         : doubt
Synonyms         : call into question, cast doubt upon, challenge, controvert, disbelieve, dispute, distrust, hesitate, impeach, impugn, mistrust, oppose, puzzle over, query, suspect, suspicion, wonder about
Antonyms         : certainty, doubtlessness, sureness, surety

 

FORMATS OF QUESTIONS ON SYNONYMS

FORMAT 1:
* Choose the word/group of words which is most nearly the SAME in meaning as the word/group of words given in bold as used in the passage. (In this case, a word for choosing the synonym is taken from the passage meant for Reading Comprehension.)

e.g. tore out
           1. came out gently
           2. pushed out
           3. walked out
           4. rushed out forcefully
           5. destroyed angrily
Ans.  tore out : (4) rushed out forcefully

 

FORMAT 2:
* In each of the following questions, out of the given alternatives, choose the one which best expresses the meaning of the given word.

 

e.g. ABNEGATION
             a. self-denial
             b. self-sacrifice
             c. self-praise
             d. self-criticism
Ans. ABNEGATION: (a) self-denial

 

FORMAT 3:
* In each of the following questions, there are three words which are meanings of a certain
word. Select that word from the answer choices provided in each question.

 

e.g. everlasting, endless, unending
             (a) living
            (b) eternal
            (c) increased
            (d) durable
Ans. everlasting, endless, unending: (b) eternal

 

FORMAT 4
* In each of the following questions, there are four words marked a-d. While three of them are synonymous or have more or less same meaning, one is altogether different from the rest. Select from the answer choices the word which is different from the rest.
 e.g.  (a) witty   (b) pleasant (c) comical (d) humorous                                   
Ans. (b) pleasant

 

FORMAT 5
* In each of the following questions, four pairs of words are given, marked a-d. Each pair consists of two words which have more or less similar meaning. However, one pair consists of two words which are different in meaning, which you have to select as your answer.
 e.g.  (a) authentic/genuine (b) genius/aptitude (c) ghastly/crime (d) gruesome/grim
Ans.  (c) ghastly/crime

 

FORMAT 6
* In each of the following questions, a sentence is given in which one word is printed in bold type. Under each sentence four alternatives, marked a-d are given. Your task is to select the word or expression from the alternatives which convey more or less same meaning as the word printed in bold type.
e.g. The U.N. coalition forces immediately went into action. (a) most powerful (b) faithful (c) temporary alliance (d) selective
Ans.  (c) temporary alliance

Vocabulary

Vocabulary: Meanings (synonyms)
1. Mrs Bates tried to domesticate Anna.
    Domesticate → to make (an animal) able to live with man and serve him → tam → bring under control → train


2. What God decrees we have to accept.
     Decree → command → decide → order → judgement


3. We were nonplussed that the mistress of the house had heard of the tragedy.
     Nonplussed → confused → surprised → puzzled → bewildered → dazed


4. They endeavoured to explain it as an act of charity.
    Endeavour → strive → try hard → make an effort → attempt → struggle


5. All this played real havoc on our imagination. 

 Havoc → destruction → disturbance → disorder → disaster → devastation → chaos


6. I found that I could scarcely breathe.
    Scarcely → barely → almost not → hardly → (only) just


7. It was an eternal mystery to us.
    Eternal → forever → always → never ending → endless → everlasting → incessant → continual


8. God had taken the baby at such a tender age.
     Tender → delicate → young → child-like → gentle


9. We shuddered as we gnawed at the hunk of meat.
     Shudder → tremble → quiver → shake → shiver → tremor


10. The dog snarled at the intruder.
      Snarl → scowl → growl → threaten → intimidate → scare

 

Choose the alternative that best fits the blank:
1. The dancers were in Japanese __________. (outfit, dress, costume)
2. He is a wolf in the ___________ of a sheep. (attire, costume, garb)
3. She came to the party ________ her new diamond necklace. (showing, sporting, having)
4. We recognised him to be a policeman by his_________. (attire, uniform, garment)
5. The beggar's _________ were in tatters. (clothes, dress, costume)

 

Conditional clause ('If ' clause):
Conditional clauses are classified into three types based on the tenses.
They are:   1. Probable (possible) condition
              2. Improbable condition
              3. Unfulfilled condition

 

Type - I
Probable / possible condition

Usage: We use this type to talk about the future activities that are quite possible.
Structure: If (Subject + V1  →   Subject + can / will / may + V1)
           e.g: If you work hard,               you can get the first rank.
            Simple present tense               Simple future tense
1. Walk fast or you will miss the bus.
               If you walk fast,                    you will not miss the bus.
               sub + V1                             sub + will + V1
               Unless you walk fast, you will miss the bus.
                                   (unless = if not)

2. Take the medicine regularly or you may fall ill again.
         → If you take the medicine regularly you may not fall ill again.
         → Unless you take the medicine regularly, you may fall ill again.


Type - II
Improbable / Imaginary condition

Usage: We use this type to talk about the actions that we think are possible but not very
 probable. It indicates that we do not expect the action in the If-clause to take place.
Structure: If (Subject + V2 → Subject + could / would / might + V1)
                   e.g: If I were a doctor,    I could give you treatment.
                                   V2                            V1
Note:     [  V1         V2          V3]
            is          are         been
                        are       were
e.g: 1) I am not a bird. So, I can' t fly in the sky.
         → If I were a bird,                I could fly in the sky.
         V- Simple past tense               conditional past

 Note: [ The above sentence is quite imaginary. It is not possible, i.e., unreal]
            2) I don't have money. So I can't give you any.      (March 2003)
             → If I had money,                    I could give you some / any.
                          V2                          conditional past
Note:       [  V1         V2         V3]
              have      had        had
                         has
[The above sentence is not possible for that situation, but quite imaginary]
3) I don't have time. So, I can't accept the job.
   If I had time,     I could accept the job.


Type - III
Unfulfilled condition

Usage: We use this type to talk about past actions that didn't happen. It expresses a condition in the past that hasn't been fulfiled (Unfulfilled).
Structure: If [ subject + had + V3 → subject would have / could have / might have + V3]
                  

                   e.g: If you had asked me,               I would have helped you.
                       Past perfect tense                     Perfect conditional tense
1. He didn't study well. So, he failed.                                                              
    → If he had studied well, he would not have failed.


2. She didn't carry her driving license. So, she had to pay a fine.
     → If she had carried her driving license, she would not have had to pay a fine.


3. You didn't take the medicines regularly. So, you fell ill again.
    → If you had taken the medicines regularly, you would not have fallen ill again.


4. I was held up in a traffic jam. So, I missed the train.                                        
    → If I had not been held up in a traffic jam, I would not have missed the train.


5. No precautions were taken. So, many were killed in the cyclone.
    → If precautions had been taken, many would not have been killed in the cyclone.


Notice the following structures:
         Type I         Sub + V1             Sub + will
         Type II       Sub + V2             Sub + would
         Type III     Sub + had + V3   Sub + would have           

                       If you invite me,   I will attend the party.
                                    V1
                       If you invited me,   I would attend the party.
                                       V2
                       If you had invited me,   I would have attended the party.
                                   had + V3

ఎస్‌బీఐ అప్రెంటిస్‌ నోటిఫికేషన్

ఎస్‌బీఐ అప్రెంటిస్‌ దరఖాస్తు ఎలా

DATA COMMUNICATION AND NETWORKS

Introduction
Information is carried out in data communication systems as signals between two or more points. To understand transmission one needs to study electrical form that the messages take while they are in transit and of media and transmission technologies.
Signals: Signals are electric or electromagnetic encoding of data, and signalling is propagation of signal along suitable communication medium.
Transmission: Transmission is communication of data achieved by the propagation and processing of signals.
Parallel and Serial Transmission:
           In parallel data transmission, there are multiple parallel lines connecting the transmitting and receiving units. Each wire carries a bit of information. 
           In series data transmission, each bit is sent sequentially one after another and it requires one pair of wires for connecting the receiving and transmitting units.
Series transmission is slower than parallel transmission and is used primarily for transferring data between devices at the same site. Communication between computers is almost always serial.
Synchronous and Asynchronous Transmission: The mode of transmission is the way in which coded characters are assembled for the purpose of transmission and permits receiving devices to identify where the coding for each character begins and ends within the torrent of bits. When two computers communicate, they must have a way to synchronize the flow of data so that the receiving computer can read at the same speed at which the sending computer transmits.
           In synchronous transmission characters are transmitted as groups, with control characters in the beginning and at the end of the bit train. The transmission and receiving intervals between each bit are precisely timed permitting the grouping of bits into identifiable characters. In synchronous mode, intervals between characters are uniform within space between consecutive bytes.
           In asynchronous transmission, each character is transmitted separately, that is, one character at a time. Each character begins with a start bit and ends with a stop bit.
The start and stop bits and the interval of time between consecutive characters allow the receiving and sending computers to synchronize the transmission.
Simplex, Half-duplex, Full-duplex Communication
In Simplex mode, the communication channel is used in one direction. The receiver receives the signals from the transmitting device. The simplex mode is rarely used for data communication.
In Half-duplex mode, the communication channel is used in both directions, but in one direction at a time. This requires the receiving and transmitting devices to switch between send and receive modes after each transmission.
In Full-duplex mode, the communication channel is used in both directions at the same time. Typical example of this mode of transmission is the telephone in which both parties talk to each other at the same time.
Local Area Network (LAN): A LAN is a data communication network, which connects many computers of workstations (computer terminal, printer etc.) and permits exchange of data and information among themselves, within a localised area, typically confined to a building, or a cluster of buildings.
LAN topology: A network topology refers to the physical layout of the network in which all the devices are connected. This includes all the hardware that makes up the network. The points of connection to the network by the stations are called Nodes or link stations. There are several types of typographical design and strategies used to implement LAN. The majority of these are based on three types of topologies:
*  Star       
*  Bus  
*  Ring
Star Topology: In this topology, a number of stations are connected directly to a central station or controller. Communications on the connecting links between the stations and the central station of a star topography can be bi-directional and are point-to-point.
A station on this type of network passes an information to the central controller, which then forwards the information to the destination station. The central controller manages and controls all communications between stations on the network.
Bus Topology: All stations are connected to a single communication line. This single communication line is referred to as a bus. Information frames originating at a station are propagated away from the station in both directions on the bus. Each station on the bus interrogates the information frame destination address field for its own address. If the destination address field matches the station address, only then it accepts the information frame and processes the frame.
Ring Topology: Local area networks that have each station attached to an adjacent station using point-to-point links form a physical ring. Each station attached and active to the ring
regenerates the information frame, and then re-transmits the information frame on the ring. The ring itself is logically circular and the information travels in one direction.
              Failure of a station in a ring topology disrupts the ring because the information frame is not regenerated. Additions or deletions of stations to the ring can be disruptive, if the changes are not managed properly.
Lan Access Method: Access methods are the means or way by which stations actually gain the use of the common channel to transmit messages. The right to transmit is an issue only in broadcast where work stations share a single channel.
              Many techniques have been proposed, but two of these are commonly used.
*   Carrier-Sense Multiple Access with Collision Detection (CSMA/CD)
*   Token passing.
CSMA/CD: CSMA/CD access method is used with bus networks. The bus operates in a Multiple Access (MA) mode. A node is allowed to transmit on the bus, if it senses that the medium is free (carrier sense). Occasionally, two or more nodes may simultaneously sense that the medium is free and begin to transmit. This creates a collision as the contents of transmitted information frames will collide resulting in corruption of the information frame. This collision is detected (collision detection) by the transmitting node. The two (or more) nodes involved then wait for a further short random time interval before trying to retransmit a frame.
Token Passing: Another way of controlling access to a share medium is by the use of a control (permission) token. The control token is passed from one node to another according to a defined set of rules understood and adhered to by all nodes.
In token passing, a logical ring of all nodes connected to the physical medium is first established and a single token is generated; The control token passes from one node to another traversing the logical ring. The token keeps on circulating the logical ring until it is received by a node waiting to send an information frame. After receiving the token, waiting station transmits its waiting frames on the physical medium after which it passes the control token to the next node in the logical ring.
Wide Area Network: A Wide Area Network, or WAN, is a network that links separate geographical locations. A WAN can be a public system such as the Public Switched Telephone Network (the PSTN) or one of the various packet switched services provided by the public telecommunication authorities. WANs can also use most other types of circuit including satellite networks, ISDN, Value Added Networks (VANs/ VADs).
            The main distinguishing feature between a WAN and LAN is that the LAN is under the complete control of the organisation which owns it, whereas the WAN needs the involvement of another authority like the telephone company.
Communication Switching Techniques: In a WAN, two computing devices are not connected directly. A network of switching nodes provide a transfer path between the two devices.
The process of transferring data blocks from one node to another is called data switching.
There are three switching techniques commonly employed and these are:
* Circuit Switching: In Circuit switching there is a dedicated communication path between the sending and receiving devices. The dedicated path is a connected sequence of links between switching nodes. A conventional telephone network, where a dedicated path is set between the caller and the called party for the duration of a telephone call, is an example of circuit switching.
             Circuit switching is mainly used for voice telephone network, but is not all that effective for data communication networks, as channel capacities are not fully utilised.
* Message Switching: Message Switching is an alternative switching technique, where it is not necessary to establish a dedicated path between the sending and receiving devices. In Message Switching, the sending device appends the destination address to the message and passes it to the network; the message is then passed through the network from one node to another till it reaches the intended destination. Each switching node receives a message, stores it briefly and then transmits it to the next node. Examples of a message are electronic mails, computer files, telegrams and transaction queries and responses.
* Packet Switching: Packet Switching combines the advantages of message and circuit switching. Packet switching is functionally similar to message switching, in which data is transmitted in block,stored by the first switching node it meets in the network and is forwarded to the next and subsequent downstream nodes until it reaches the destination.
Network/ File server system: For sharing data in a LAN, users stores files on a file server. A file server is a central node (Computer in the network) that stores data files where all users can access them. Typically, the file server in LAN acts as a central hub for sharing peripherals like printers, print queues and modems. In a LAN's file server, in many cases entire files are pumped across the network on behalf of the operations taking place on LAN computers. A file server does not involve in processing of an application. It simply stores files for applications that run on LAN computer.
Client/ Server system: Any local area network could be considered as client/ server system, since the workstation (clients) requests services such as data, programme files, or printing from server. A client/ server (C/S) has three distinct components, each focussing on a specific job: a database server, a client application and a network.
 A server gives stress on efficiently managing a resource such as a database of information. Its main job is to manage its resources optimally among various clients that concurrently request the server for the same resource.

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ACTOR

      An object-oriented programming language developed by the Whitewater Group Limited. It is aimed at Microsoft Windows programming and has a Pascal-like syntax.
Adaptive Differential Pulse Code Modulation
       Abbreviated ADPCM. In multimedia, a technique used to compress digital audio samples before they are stored on disk. ADPCM stores samples as the difference between the current sample and combination of previous samples. ADPCM is used as the storage method by CD-ROM XA and CD-I disks, and is also used in cordless telephones for coding and decoding.
Adobe Illustrator
       An advanced illustration program for Macintosh and IBM - compatible computers,introduced by Adobe Systems in 1987. Adobe Illustrator produces Post Script output,and offers Bezier curves, coding for colour printing, and an automatic tracing tool, as well as many other features required for professional-quality illustration.
After Dark
    A very popular screen saver program for IBM - compatible and Macintosh computers developed by Berkeley Systems, Inc.
After Dark lets the user select the screen-saver image to use from a library of images that includes the ever-popular flying toasters.
Aftermarket
      The market for related hardware, software, and peripherals created by the sale of a large number of computers of a specific branch.
Abort, Ignore, Retry, Fail
      In DOS, an error message indicating some sort of problem with a device, usually a floppy disk drive.
     This is one of the most common DOS error messages you will see, and to fix it  you first have to understand why DOS is complaining. It may be that the disk drive door is open, that there is not disk in the drive, or that the disk has not been formatted yet.
     You may also see this error message with devices other than disk drives - for example, if you try to send text to the printer using the DOS COPY command, but the printer is not online.
Append
     The operation of adding information to the end of an existing file. For example, in dBASE, the APPEND command lets users add new records at the end of a table.    
Ascending sort
     Asort operation that organizes data in order from smallest to largest number, from first to last date, or in normal alphabetical order, depending on the type of date sorted.
Descending sort
    A sort operation that organizes data in reverse alphabetical, numeric, or date order, depending on the type of data sorted.
Aspect ratio
    In computer graphics, the width-to-height ratio of an image or computer screen; a ratio of 2:1 indicates that the width is twice the height. Aspect ratio becomes important in preventing distortion when an image is resized or incorporated into another document.
Assembler
    A program that converts an assembly language program into machine language so that the computer can run the program.
Attribute
    A file attribute is a characteristic that indicates whether the file is a read-only file, a hidden file, a system file, or has changed in some way since it was last backed up.
Authoring program
    In programming a high-level language used to develop multimedia presentations that contain graphics, audio, text animation, and video elements.
Batch file
     An ASCII text file containing operating system commands and possibly other commands supported by the batch processor. The commands in the file are executed one line at a time, just as if you had typed them at the system prompt. You can include program names, operating system command, batch language commands, and other variables in your batch files. Batch files are used to automate repetitive tasks.
Autoexec.Bat
      A contraction of AUTOmatically EXECuted BATch. A special DOS batch file, located in the root directory of your startup disk, that runs automatically every time you start or restart your computer.
     As with all batch files, the commands contained in Autoexec.Bat are one by one just as if you had typed them at the system prompt.
Autoflow
     In desktop publishing and word processing, flowing text continuously into columns often around anchored graphics.
Config.sys
     In DOS and OS/2, a special text file containing settings that control the way that the operating system works. Config.sys must be located in the root directory of the default boot disk, normally drive C, and is read by the operating system only once as the system starts running.
Boot
     The loading of an operating system into memory, usually from a hard disk, although occasionally from a floppy disk. This is an automatic procedure begun when you first turn on or reset your computer. A set of instructions contained in ROM begin executing, first running a series of power on self tests (POST) to check that devices such as hard disks are in working order, then locating and loading the operating system, and finally, passing control of the computer over to that operating system.
Bootable disk
     Any disk capable of loading and starting the operating system, although most often used when referring to a floppy disk. In these days of larger and larger operating system, it is less common to boot from a floppy disk. In some cases, all of the files needed to start the operating system will not fit on a single floppy disk, which makes it impossible to boot from a floppy.
Boot record
    That part of a formatted disk containing the operating system loading program, along with other basic information needed by the computer when it starts running.
Backup
    An up-to-date copy of all your files that you can use to reload your hard disk in case of an accident. It's an insurance against disk failure affecting the hundreds or possibly thousands of files you might have on your system hard disk, or on your local area network hard disk.
Backup command
    A DOS and OS/2 command that lets you make a backup, or archive copy, of files and directories on your system.
   The backup command can save all your work, file by file, directory by directory, from one disk to another. If, after you have made a backup, you find you have to retrieve a file from the backup, you must use the RESTORE command.
Bad sector
     An area on a hard disk or floppy disk that cannot be used to store data, because of a manufacturing defect or accidental damage. One of the tasks an operating system performs is finding, marking, and isolating bad sectors. Almost all hard disks have some bad sectors, often listed in the bad track table, as a result of the manufacturing process, and this is not usually anything to worry about; the operating system will mark them as bad, and you will never even know that they are there.
Bar code
     A machine-readable numerical code, printed as a set of varying-width vertical bars, used to identify items as diverse as grocery products and library books. A bar code reader scans the bar code, and converts it into a number that the computer can then process and display on screen.
Bounce
     The return of an e-mail message to its original sender due to an error in delivery.This may be due to a simple spelling mistake in the e-mail address, the recipient's computer system may be down, or they may no longer subscribe to or have an account on the system.
    The returned e-mail will usually contain a description of why the message bounced.
Bar code reader
     An input device used to read bar codes. The device may be a light pen or stylus that scans the code, or a non-contact optical or laser unit. The bar code is read and converted into a number that the computer can process for inventory control and other statistical information
Bandwidth
   In communications, the difference between the highest and the lowest frequencies available for transmission in any given range.
   In networking, the transmission capacity, of a computer or a communications channel, stated in megabits or megabytes per second; the higher the number, the faster the data transmission.
Baseband network
     In networking, a method of transmitting signals as a direct-current pulse rather than as a modulated signal.
    In a baseband network, because the entire bandwidth of the transmission medium is used by a single digital signal, computers can transmit only when the channel is not busy. A baseband network can operate over relatively short distances (upto 2 miles if network traffic is light) at speeds from 50 Kilobits per second upto 16 megabits per second.
Band
    A measurement of data-transmission speed. Originally used in measuring the speed of telegraph equipment, it now usually refers to the data-transmission speed of a mode or other serial device.
Ethernet
      It is a popular network protocol and cabling scheme with a transfer rate of 10 megabits per second.
     Ethernet uses a bus topology capable of connecting upto 1024 PCs and workstation within each main branch. Network nodes are connected by using either thick or thin coaxial cable, or by twisted-pair wiring.
Broadband network
    It is a technique for transmitting a large amount of information, including voice, data, and video, over long distances.
    The transmission capacity is divided into several distinct channels that can be used concurrently, normally by using frequency-division multiplexing, and these individual channels are protected from each other by guard channels of unused frequencies. A broadband network can operate at speeds of upto 20 megabits per second, and is based on the same technology as used by cable television.
Multiplexor
      Often abbreviated mux. In communications, a device that merges several lowerspeed transmission channels into one high-speed channel at one end of the link. Another multiplexor reverses this process at the other end of the link to reproduce the low-speed channels.
This is of following types:
Frequency-division multiplexing: A method of sharing a transmission channel by dividing the bandwidth into several parallel paths, defined and separated by guard bands of different frequencies. All signals are carried simultaneously.
Time-division multiplexing: A method of sharing a transmission channel by dividing the available time equally between competing stations. At the receiving end, the different signals are merged back into individual streams.
Statistical multiplexing: A method of sharing a transmission channel by using statistical techniques to allocate resources. A statistical multiplexor can analyse traffic density, and can dynamically switch to a different channel pattern to speed up the transmission. At the receiving end, the different signals are merged back into individual streams.
Benchmark
     A test that attempts to quantify hardware or software performance-usually in terms of speed, reliability, or accuracy. One of the major problems in determining performance is deciding which of the many benchmarks available actually reflects how you plan to use the system.
Benchmark program
   An application program that attempts to provide a consistent measurement of system performance. These programs include Dhrystone (microprocessor and memory performance); Whetstone (speed of arithmetic operations); and Khornerstone (overall system performance, including disk drive access speed, memory access speed, and processor performance).
Beta software
    Software that has been released to a cross-section of typical users for testing before the commercial release of the package.
Buffer
     An area of memory set aside for temporary storage of data, often until some external event completes. Many peripherals, such as printers, have their own buffers. The computer transfers the data for printing from memory into the buffer, and the printer then processes that data directly from the buffer, freeing the computer for other tasks.
Modulation
     The process used by a modem to add the digital signal onto the carrier signal, so that the signal can be transmitted over a telephone line.
     The frequency, amplitude, or phase of a signal may be modulated to represent a digital or analog signal.
Demodulation
     The process of retrieving the data from a modulated carrier signal; the reverse of modulation.
Carrier signal
     Asignal of chosen frequency generated to carry data, often used for long-distance transmissions. The data is added to this carrier signal by modulation, and decoded on the receiving end by demodulation.
Bug
    A logical or programming error in hardware or software that causes a malfunction of some sort. If the problem is in software, it can be fixed by changes to the program. If the fault is in hardware, new circuits must be designed and constructed. Some bugs are fatal and cause the program to hang or cause data loss, others are just annoying, and many are never even noticed.
Bridge
      In networking, a hardware device used to connect local area networks (even networks using different wiring or network protocols) together so that they can exchange data. A bridge operates at the data-link layer of the International Standards Organisation's Open Systems Interconnection (ISO/OSI) model for computer-to-computer communications, and manages the flow of traffic between the two local area networks by reading the address of every packet of data that it receives.
Router
      In networking, an intelligent connecting device that can send packets to the correctlocal area network segment to take them to their destination. Routers link local area network segments at the network layer of the International Standards Organisation's Open Systems Interconnection (ISO/OSI) model for computer-to-computer communications.
Brouter
       In networking, a device that combines the attributes of a bridge and a router. A brouter can route one or more specific protocols, such as TCP/IP, and bridge all others.
Burst mode
     In communications, a method of data transmission in which information is collected and then sent in one single high-speed transmission, rather than one character at a time. Systems that use multiplexors to serve several channels often use burst mode to service each channel in turn.
Gateway
       In networking, a shared connection between a local area network and a larger system, such as a mainframe computer or a large packet-switching network. Usually slower than a bridge or router, a gateway typically has its own processor and memory, and can perform protocol conversions. Protocol conversion allows a gateway to connect two dissimilar networks; data is converted and reformatted before it is forwarded to the new network.

INTERNET

          The Internet is global collection of people's computers, which are linked together by cables and telephone lines making communication possible among them in a common language. However, the rigid technological definition of Internet is that it is a global collection of interconnected networks. By definition, a network allows computer users to share computer equipment and programs, messages, and the information available at one site.
How does Internet Work?
        A computer network by definition allows sharing of resources. Since all softwareresources exist in computers in the form of files of data, one of the key aspect in network of many computers is to move data between two specific computers. For such a communication, we require:
* The address of the destination.
* a safe means of moving data in the form of electronic signals. 
As far as safe movement of data is concerned, there exists a set of rules, which govern the sending and receiving of data on the Internet. These rules are implemented in two parts in the networks software and are called Transmission Control Protocol (TCP) and Internet Protocol (IP). These two are collectively called TCP/IP. For sending a large block of text/data to another machine, TCP divides the data into little data packets. It also adds special information, e.g. the packet position, error correction code etc., to make sure that packets at the destination can be reassembled correctly and without any damage to data. The role of IP here is to put destination-addressing information on such packets. 
      The following can be a typical person-understandable address on Internet: user name@host.domain
       The user name in general is the name of the Internet account. This name is same as the one, which you may use when logging into the computer on which you have your Internet account (Logging in is the process of gaining access to your account on a computer, which is shared by several users). Your Internet account is created on it.
       Hosts are in general, individual machines at a particular location. Resources of a host machine is normally shared and can be utilised by any user on Internet.
Domains are general category that a computer on the Internet belongs to. The most common high level domains are .com, .org etc.
Tools & Services on Internet
       To work with Internet and to utilise some of the points mentioned above we use certain tools. For example, Telnet is a tool, which is utilised for logging on remote computers on the Internet.
Electronic Mail
       One of the very useful things about the Internet is that it allows you almost instant
exchange of electronic message (e-mail) across the world. E-mail is mainly used for sending electronic piece of text.
USENET and News Groups
      On Internet there exists another way to meet people and share information. Onesuch way is through USENET newsgroups. These are special groups set up by people who want to share common interests ranging from current topics to cultural heritages.
      The newsgroups are really meant for interaction of people who share your interests.
You can post your own questions as well as your answers to the questions of others, on the USENET.
Frequently Asked Questions (FAQ)
         Agreat resource offered by USENET is the FAQs, that is the list of frequently asked questions and responses for them for particular newsgroup. FAQs are an excellentsharing place for learning about a topic.
          These FAQs are generally text files or USENET articles.
Connecting to Remote Machine with Telnet 
         Telnet is a program that allows an Internet host computer to become a terminal of another host on the Internet. Telnet allows to become a user on a remote machine. You can run the Internet computer programs available on that machine.
Gopher
        Gopher displays a set of resources on the Internet in the form of menus or lists of items. You go around the Internet by selecting items from these menus. You need not know the addresses and commands. You just select an item of interest to see its content on the screen.
HTML 
        The Hyper Text Markup Language (HTML) is a language used for creating documents
for the World Wide Web. Although most browsers will display any document that is written in plain text, there are advantages to writing documents using HTML. When HTML documents are read by applications specifically designed for the WWW, they can include formatting, graphics and even links to other documents and websites on the World Wide Web.
SGML
        Standard Generalised Markup Language (SGML) is used for defining the structure and managing the contents of any digital document. HTML used in many world wide web document on the Internet is a part of SGML.
World Wide Web
       It is a huge collection of hyper text pages on the Internet. It is one of the most flexible and exciting tools in existence for surfing the Internet.
      Hyper text link connects the pieces of information (text, graphics, audio or video) in separate HTML pages created at the same or at different Internet sites.
HTTP
      Hyper Text Transport Protocol (HTTP) is used to manage the links between one hyper text document and another.
      HTTP is the mechanism that opens the related document when you click on a hyper text link, no matter where on the Internet that related document happens to be.
Home Page
     It is an initial starting page. A home page on the Internet may be related to a single person, a specific subject, or to a corporation, and is a convenient jumping-off point
to other pages or resources.
URL
    Uniform Resource Locater (URL) is a method of accessing Internet resources. URLs contain information about both the access method to use and also about the resource itself, and are used by web browsers to connect you directly to a specific document or page on the World Wide Web, without you having to know where that resources is located physically.
Veronica
    A search service built into the Gopher Internet application. When you use Veronica to search a series of Gophermenus (files, directories, and other items), the results of the search are presented as another Gopher menu, which you can use to access the resources your search has located. Veronica supposedly stands for Very Easy Rodentoriented Net-wide Index to computer Archives.
WAIS:
     Abbreviation for Wide Area Information Service, pronounced "ways". A service used to access text databases or libraries on the Internet.
    WAIS uses simple natural-language queries, and takes advantage of index searches for fast retrieval. Unlike Gopher, which only searches through the names of Gopher resources, WAIS can search the content of all documents retrievable from WAIS databases. WAIS is particularly adept at searching through collections of articles, USENET newsgroups, electronic texts and newspaper archives.
Browser: An application programme used to explore Internet resources.
A browser lets you wander from node to node without concern for the technical details of the links between the nodes or the specific methods used to access them, and presents the information- text, graphics, sound, or video - as a document on the screen.
Web browser: A World Wide Web client application that lets you look at hyper text documents and follow links to other HTML documents on the Web. When you find something that interests you as you browse through a hyper text document, you can click your mouse on that object, and the browser automatically takes care of accessing the Internet host that holds the document you requested; you don't need to know the IP address, the name of the host system, or any other details.
Mosaic: It is a World Wide Web client program. Mosaic uses a graphical user interface to give access to Internet resources, and allows users to navigate through hyper text documents quickly and easily using a mouse.
FTP: Abbreviation for the File Transfer Protocol. The protocol used to access a remote Internet host, and then transfer files between that host and your own computer. FTP is also the name of the program used to manage this protocol. FTP is based on client/ server architecture;
you run an FTP client program on your system, and connect with an FTP server running on the Internet host computer.
Archie: A system used on the Internet to locate files available by anonymous FTP. Once a week, special programs connect to all the known anonymous FTP sites on the Internet and collect a complete listing of all the publicly available files. This listing is kept in an Internet archive database, and when you ask archie to look for a file, only this database is searched rather than the whole Internet; you can then use anonymous FTP to retrieve the file.
Modem: Contraction of modulator/ demodulator; a device that allows a computer to transmit information over a telephone line. The modem translates between the digital signals that the computer uses, and analog signals suitable for transmission over telephone
lines. When transmitting, the modem modulates the digital data onto a carrier signal on the telephone line. When receiving, the modem performs the reverse process, and demodulates the data from the carrier signal.
Internal modem: A modem that plugs into the expansion bus of a personal computer.
External modem: A stand-alone modem, separated from the computer and connected by a serial cable.
LEDs on the front of the chassis indicate the current modem status, and can be useful in troubleshooting communications problems.
X-modem: In communication, a popular file transfer protocol available in many off the- shelf and shareware communications packages, as well as on many bulletin boards.
         X-modem divides the data for the transmission to blocks; each block consists of the start-of-header character, a block number; 128 bytes is returned to the sender if the check sum calculation is identical to the sender's check sum; however, this requirement to acknowledge every block can cause poor performance.
        An extension to X-modem, called X-modem-CRC, adds a more stringent errorchecking method by using a cyclical redundancy check to detect transmission errors rather than X-modem's simple additive check sum.
Y-modem: Y-modem, a variation of the X-modem protocol, divides the data for thetransmission into blocks; each block consists of the start-of-header character, a block number, 1K of data, and a check sum. Y-modem's larger data lock means less overhead for error control when compared with X-modem, but if the block has to be retransmitted because the protocol detects an error, there is more data to resend.
Y-modem also incorporates the ability to send multiple files in the same session, and to abort file transfer during the transmission.
Z-modem: Z-modem is similar to X-modem and Y-modem but is designed to handle larger data transfer with fewer errors, Z-modem also includes a feature called checkpoint restart that allows an interrupted transmission to resume at the point of interruption, rather than starting again at the beginning of the transmission. If you have a choice between several protocols, choose Z-modem if you can; it is fast as well as convenient.
Newbie: A newcomer coming to Internet world is known as a newbie.
Netiquette: A contraction of network etiquette. The set of unwritten rules governing the use of e-mail, USENET news groups, and other online services.
USENET
       Contraction of USEr NETwork an international, non commercial network, linking many thousands of Unix sites.
       Although there is a very close relationship between the Internet and USENET, they are not the same thing by any means.
USENET predates the Internet; in the early days, information was distributed by dial - up connections. Not every Internet computer is part of USENET, and not every USENET system can be reached from the Internet.
        Like the Internet, USENET has no central governing body; USENET is run by the people who use it.
Moderated Newsgroup
        On the Internet, a USENET newsgroup of mailing list which is managed by one or more people in an attempt to maintain standards for the newsgroup. All posts to the newsgroup are reviewed by the moderator to make sure that they meet the standards the newsgroup has set for subject and commercial content before being passed on to the whole group. Moderation is not censorship, but an attempt to avoid some of the more extreme antics of those who enjoy flaming and flame wars.
Moderator
         A person or small committee of people who review the contents of all posts to a USENET newsgroup or mailing list in an attempt to ensure that the postings meet the standards set by the group.
Moderators are almost always volunteers.
Unmoderated newsgroup
         A USENET newsgroup or mailing list in which posts are not subject to review before distribution. You will find the discussions in unmoderated newsgroups to be wildly spontaneous, but they will also contain more than their fair share of flames and flame wars.
Flame
       A deliberately insulting e-mail message or post to a USENET newsgroup, usually containing a personal attack on the writer of an earlier post. Flames are often generated by established newsgroup members when a newbie posts a question which is answered in the newsgroup's FAQ.
Flame bait
       An insulting or outrageous posting to a USENET newsgroup specifically designed to provoke other subscribers into flaming the originator.
Flame war
      A prolonged series of flames in a USENET newsgroup which may have begun as a creative exchange of views but which quickly degenerates into personal attacks and crude name - calling.
Post
        An individual article or e-mail message sent to a USENET newsgroup or to a mailing list, rather than to a specific individual. Post can also refer to the process of sending the article to the newsgroup.
Anonymous posting
       In a USENET newsgroup, a public message posted via an anonymous server in order to conceal the identity of the original author. This server removes all the information from the message that could identify the sender, and forwards the message to its destination. If you ever use an anonymous server, don't forget to remove your signature from the bottom of your posting.
Mime
       Abbreviation for Multipurpose Internet Mail Extensions. A set of extensions that allows Internet e-mail users to add non - ASCII elements such as graphics, post script files, audio or video to their e-mail. Most of the common e-mail client programs include mime capabilities.
Anonymous FTP    
          Amethod of accessing an internet computer with the FTP (file - transfer program) which does not require that you have an account on the target computer system. Just login to the Internet computer with the uఅser name anonymous and use your e-mail.

ఇవి చేయకండి

బ్యాంకు పరీక్షలో విజయం సాధించాలంటే అభ్యర్థులకు ఏమి చేయాలన్నదానితో పాటు ఏమేం చేయకూడదో కూడా తెలియటం తప్పనిసరి. అవేమిటో చూద్దాం. 
‣ ప్రిపరేషన్‌ ఎక్కడ, ఎలా మొదలు పెట్టాలో తెలియకపోవడం
‣ టైమ్‌టేబుల్‌ అనుసరించకపోవడం
‣ తాము నిర్దేశించుకున్న పరీక్షా ప్రణాళికను వదిలివేయడం
‣ కేవలం రోజులో ఎన్ని గంటలు చదివామో అని మాత్రమే గమనించుకోవడం
‣ కొన్ని విభాగాలను అశ్రద్ధ చేయడం
‣ అన్ని కాన్సెప్టులపై పట్టులేకపోవడం
‣ తాము బాగా చేయగలిగే టాపిక్స్‌పై నిర్లక్ష్యం వహించడం
‣ మోడల్‌ పేపర్లు/ ప్రీవియస్‌ పేపర్లు సాధించకపోవడం
‣ రాసిన మోడల్‌ పేపర్‌ను విశ్లేషించుకోకపోవడం
‣ పరీక్షా విధానంలోని ఆన్‌లైన్‌ టెస్టులను సాధన చేయకపోవడం
‣ టాపిక్స్‌ను రెగ్యులర్‌గా పునశ్చరణ (రివిజన్‌) చేయకపోవడం
‣ పరీక్ష రాయటంలో తమ వేగం, కచ్చితత్వం గమనించుకోకపోవడం, వాటిని మెరుగుపరుచుకోకపోవడం
‣ ప్రతిరోజూ వార్తాపత్రికలు చదవకపోవడం. కరెంట్‌ అఫైర్స్‌, ఫైనాన్షియల్‌/బ్యాంకింగ్‌ వార్తలను పట్టించుకోకపోవడం
‣ దృష్టినంతా ప్రిలిమ్స్‌ పరీక్ష పైన మాత్రమే పెట్టడం
‣ సోషల్‌మీడియాను వదల్లేక దానిలో విలువైన సమయం వృథా చేయడం
‣ లక్ష్యసాధనకు అవసరమైన ప్రేరణను పరీక్ష రాసేవరకూ కొనసాగించకపోవడం
వీటన్నింటినీ అనుకూలంగా మార్చుకుంటే ఫలితం తప్పక వస్తుంది. అభ్యర్థులూ.. గుర్తుంచుకోండి- విజయం సాధించాలంటే మీరు మాత్రమే కష్టపడాలి. వేరెవరో మీకోసం ఏమీ చేయలేరు!

Simplfications

Simplifications are very important in Bank Exams. In Quantitative Aptitude /Numerical Ability section, about 40 − 50% of questions in clerical exam and about 20 − 25% of questions in Probationary Officers exam will be of simplifications. 

All simplification questions are to be solved based on BODMAS rule only.
      B − Bracket
      O − Of
      D − Division
      M − Multiplication
      A − Addition
      S − Subtraction
     When there are more brackets in the given expression, simplification should be started from inner most bracket to the outer most bracket.
Some Important Identities 

* (a + b)2 = a2 + b2 + 2ab
* (a − b)2 = a2 + b2 − 2ab

* (a + b) (a − b) = a2 − b2
*(a + b)3 = a3 + b3 + 3a2 b + 3ab2
* (a − b)3 = a3 − b3 − 3a2 b + 3ab2
* a3 + b3 = (a + b) (a2 − ab + b2)
* a3 − b3 = (a − b) (a2 + ab + b2)
* (a + b + c)2 = a2 + b+ c2 + 2ab + 2bc + 2ac
* a3 + b3 + c3 − 3abc = (a + b + c) (a2 + b2 + c2 − ab − bc − ac)
Laws of Indices 

Squares and Cubes of numbers are very useful in simplification questions. Following table gives squares and cubes of 25 numbers

Time & Work

Work is always taken as one unit. Construction of a building, filling water in the tank, painting a room etc.

To complete a job, a man will do the same amount of work on each day of the total number of days he takes to complete that job.
If a man can do a piece of work in 8 days, then his one day’s work is  .
If a man’s one day’s work is  then he can complete the total work in 4 days.
If a man can complete a piece of work in A days and another man can complete the  same work in B days,
then they together can complete the work in   days.
Similarly, three persons A, B and C together can complete in   days.
Ex: A can complete a piece of work in 6 days and B in 8 days. In what time they complete if they work together?


MAN DAYS: 
If 6 men can complete a work in 4 days, then the number of man days required to complete that work is 6 × 4 = 24.
Whatever may be the number of persons working on that, the total number of man days required for that work will be 24.
Ex:18 men together can complete a work in 14 days. In how many days 12 men finish that work?
A) 5 dyas       B) 6 days     C) 10 days       D) 8 days      E) None of these

Men and Time are inversely proportional i.e., when more men work, they take less time to complete the work. Similarly when less men work, they take more time to complete the work.
       Men and Work are directly proportional i.e., when more men are there, they do more work and less men are there, they do less work.
Similarly, Time and Work are also directly proportional. If men work for more time then they do more work and less time then the work is also less.
The relation among these variables can be shown in a formula
If M is Men, D is Days (Time) and W is work then 

Ex:  A contractor employs 12 men to complete a work in 15 days. But after 8days he notices that only 30% work has been completed. In order to finish the work in the given time, how many more men he has to recruit?
A) 32         B) 24         C) 20       D) 9         E) None of these


To complete the remaining work 32 men are required
Additional men required 32 - 12 = 20
Hence answer is (c)


PIPES AND CISTERNS
       The problems in pipes and cisterns are almost the same as those of Time and Work problems.
Ex: If a pipe fills a cistern in 12 hours and a leak in the bottom empties it in15 hours. In what time can the tank be filled when both function simultaneously?
Sol:    Pipe’s one hour’s work  =  
           Leak’s one hour’s work  =   (negative work)
           Pipe and leak together can do   work in one hour.
           Net work is Positive.
           Tank will be filled in 60 hours.


Some more models:
1. A can complete a piece of work in 240 days. A and B together can complete the same work in 144 days. In what time does B alone complete that work?
A) 15 days      B) 96 days         C) 148 days       D) 360 days         E) 240 days


2. A can do a piece of work in 12 days. B is 60% more efficient than A. In how many days B alone finish the work?


3. 14 men can do a piece of work in 12 days. 5 days after they started the work, 6 more men joined them. How many days will they now take to complete the remaining work?
A) 10 days      B) 12 days      C) 14 days     D) 8 days     E) None of these


4.   A can do a piece of work in 20 days. B can do the same work in12days. If B worked on the work for 9 days, how many days A worked on it?


5. Two pipes A and B can fill a tank in 3 and 4 hours respectively. A drain pipe C can empty a full tank in 6 hours. In what time can the tank be filled when all the three are open simultaneously?
A) 7.5 hours     B) 2.4 hours    C) 1 hours    D) 6 hours     E) None of these
Sol: A = 3 (+) , B = 4 (+) , C = 6(-)

Time and Distance

The relation among distance, time and speed is

                              Distance  =  Speed x Time.


                                     
       If a car covers 50 kilometres in each hour then the speed of the car is 50Kmph.

       If a man travels 10 metres in one second’s time the the speed of the man is 10 mps.
Convertion of speeds:         KMPH to MPS
                   

 MPS to KMPH
                                 
     When a certain distance is traveled with a speed of x kmph and another equal distance is traveled at y kmph, then the average speed = 
TRAINS
         If a train has to cross a pole or a man or any particular point  then it has to cover a distance equal to its own length.
         If a train has to cross a platform or bridge or tunnel etc. then it has to cover a length equal to its length + platform/bridge/tunnel length.
Relative speed
        When two speeds are in opposite direction,
         Relative speed = sum of the speeds.
        When two speeds are in the same direction,
        Relative speed = difference of the speeds.

BOATS AND STREAMS
Still water: water without motion. A boat can travel or a man can swim in that water with their original speeds.
Stream / current : water flow with some speed.
Down stream: along with the flow.
Upstream: against the water flow
        If the speed of the boat in still water is b kmph and speed of the current is c kmph respectively, then 

                            Downrate ( x )  =   b + c 

                            Uprate ( y )       =  b – c
                            

 Average speed
      If a moving object travels from A to B at the speed of x km/hr, and from B to A at the speed of y km/hr, then


             
Example 1:  A train 100 metre long is running at the speed of 21 km/hr and another train 150 meter long is running at the speed of 36 km/hr in the same direction. How long will the faster train take to pass the first train?
Solution:  Sum of the length of both the train =  x1 + x2 = 100 + 150        = 250 m
                                 Difference of their speeds =  y1 - y2   =  21 - 36

                                                                              
        = 15 km/hr

 Question with office concern
Example 1:  A person walking at x km/hr reaches his office t1 minutes late. If he walks at y km/hr, he reaches there t2 minutes earlier, then
            

 

 Example 5:  A man covers a distance of 160 km at 64 km/hr and next 160 km at 80 km/hr. what is his average speed for his whole journey of 320 km?

 


         

 

Example 5:  A man covers a distance of 160 km at 64 km/hr and next 160 km at 80 km/hr. what is his average speed for his whole journey of 320 km?

 

 Example 6: What will be the length of the train P when it is running at 60 km/hr and crosses another train Q running in opposite direction, in 18 seconds? In order to answer this question which of the statements (a) and (b) is/are sufficient?
              (a) Length of the train Q is 80 meter
              (b)  Speed of the train Q is 90 km/hr
Solution: Both statements (a) and (b) together are necessary
                  '.'  The trains are running in opposite directions

 

Example 7:  A boat takes 3 hours to go from P to Q downstream and from Q to P up stream. What is the speed of the boat in still water? to know the answer of this  question, the knowledge of which of the statements (a) and (b) is/are sufficient?
The distance between P and Q is 6 km.
The speed of the river is 2 km/hr.
Solution: Both statements (a) and (b) together are necessary to the question.
                  Let the speed of the boat in still water be x km/hr.
            .'.   Speed of the boat down stream = (x + 2) km/hr
       And            Speed of the boat upstream =  (x -2) km/hr

 Now x can be calculated.

                                           

Simple Interest

1. Introduction
» Money is not free and it costs to borrow the money. Normally, the borrower has to pay an extra amount in addition to the amount he had borrowed. i.e, To repay the loan, the borrower has to pay the sum borrowed and the interest.
2. Lender and Borrower
» The person giving the money is called the lender and the person taking the money is the borrower.
3. Principal (sum)
» Principal (or the sum) is the money borrowed or lent out for a certain period. It is denoted by P.
4. Interest
» Interest is the extra money paid by the borrower to the owner (lender) as a form of compensation for the use of the money borrowed.
5. Simple Interest (SI)
» If the interest on a sum borrowed for certain period is calculated uniformly, it is called simple interest(SI).

 6. Amount (A)
The total of the sum borrowed and the interest is called the amount and is denoted by A
7. The statement "rate of interest 10% per annum" means that the interest for one year on a sum of Rs.100 is Rs.10. If not stated explicitly, rate of interest is assumed to be for one year.
8. Let Principal = P, Rate = R% per annum and Time = T years. Then
                            
9. From the above formula , we can derive the followings


                                                     

Spotting Errors

There are several kinds of errors in written communication, particularly in English. These errors take place due to grammatical mistakes or slips in idiomatic usage. Grammatical errors are quite widespread. For tackling, such questions in Competitive Examinations, where English is an integral part, one should have knowledge of some common errors and rules of English grammar and usage. Hence the study material together with concepts on this topic is dealt with in detail in the item concerned.
The English language is rich and complex. There are many confusing aspects to the rules of grammar and spelling. Many words are quite similar but have very different meanings. It is almost impossible to avoid common errors in English. There are so many rules to remember and so many confusing words.
 Error free writing in English is the result of constant practice and hard work. This fact should encourage us: it means that the ability to write well is not a gift that some people are born with, not a privilege extended to only a few. If we're willing to work, we can improve our English.

Errors in English generally take place particularly in matters of -- Sequence of Tense, Punctuation, Plural Verb for Singular Subject, Nouns, Noun-Number, Possessive Case, Pronouns, Adjectives, Verbs, Adverbs, Articles, Prepositions, Question Tags, If-conditionals and so forth. As such, we need to be proficient in matters of English grammar to read, write and speak good English.
 Spotting error is an essential part of almost all the competitive examinations, which
include Test of Objective English. The foreign students of English commit some mistakes,
relating to all the important aspects of English grammar. This item, exclusively offered for
Spotting Errors, sets out to throw light on those grammatical errors which the students most frequently commit.
           It is, in this connection, an overview of the English grammar items are offered in a tabular form, which often test how good the skills of our English are. In short, we can understand that the items included in the table are popular in the realm of Spotting Errors in our written English. As such, it is important and better to have a close scrutiny of these topics from their basics to the advanced levels in terms of their usage. A standard High School English Grammar book shall be of good use in this regard.       

             In this section of the examination, sentences are given with the grammatical / the word usage and/ or the spelling errors which we are expected to identify and rectify the error part. For attempting such questions, familiarity with the basic grammar rules, including spellings and the correct usage of words is essential. Some sentences may not have any error, in which case No Error is marked as our answers.
 

Directions (Q.1-10): Under each question here, a sentence is given and divided into three parts and  named A, B and C. For each part a correction statement is also given. Read them and determine which part requires correction and mark it as your answer.
1. The Center on Wednesday moving to mollify  Dalit unrest (A)/ clearing amendments to the SC/ST(Prevention of Atrocities) Act (B)/ to nullifying the Supreme Court order of March 20 which has introduced safe guards against arrest of public servants and others (C).
A) The Center on Wednesday moved to mollify Dalit unrest
B) By clearing amendments to the SC /ST (Prevention of Atrocities) Act
C) To nullifying the Supreme Court order of  March 20 which has introduced safe guards against arrest of public servants and others.
1) A only   2) B and C  3) A and B   4) B only   5) C only

2. With the National Register of Citizens draft list leave out (A)/ 40 lakh applicants, a big political row have erupted in the country. (B)/  While the BJP has defending the NRC exercise, the Congress Party has criticised the process (C).
A) With the National Register of Citizens draft list leaving out
B) 40 lakh applicants, a big political row have erupted in the country.
C) While the BJP has defended the NRC
exercise, the Congress Party has criticized the process.
1) C only  2) B only  3) A and B  4) A only  5) A and C

3. On business matters, governments think wrong and do wrongly frequently, (A)/ they thinks right and do right a few times. (B)/ And sometimes they think rightly but do horribly wrongly, like in the draft e-commerce policy (C).
A) On business matters, governments think wrongly and do wrongly frequently.
B) They think right and do right a few times.
C) And sometimes they think right but do horribly wrongly, like in the draft e-commerce policy.
1) A only   2) B and A   3) C only   4) A and C   5) All of them

4. Do you worry that you, or your children spends too much time on social media? (A)/ Facebook and Instagram the other day said they wants to help you take control. (B)/ In a statement, the social media giants announced new tools to helping people manage their time spent on the platforms (C).
A) Do you worry that you, or your children spend too much time on social media?
B) Facebook and Instagram the other day said they want to help you take control.
C) In a statement, the social media giants announced new tools to help people manage their time spent on the platforms.
1) C only    2) A only    3) A and C   4) A and B   5) None of them

5. Today's Britain and find itself in a different era. (A)/ The vote for Brexit has committed it to leaving its biggest trading partner (B)/ and snuggling closer to others, while including a less-welcoming America (C).
A) Today's Britain finds itself in a different era.
B) The vote for Brexit has been committed it to leaving its biggest trading partner.
C) and snuggling closer to others, including a less -welcoming America. 
1) C only  2) B only  3) B and C  4) A only  5) A and C

6. One reason Donald Trump is inviting acres of commentary (A)/ is that he keep the world guessing what he means (B)/ and where his foreign policy is heading (C).
A) One reason Donald Trump invites acres of commentary 
B) is that he kept the world guessing what he means
C) and that his foreign policy is heading.
1) A and B    2) B and C    3) C only   4) A and C   5) All of them

7. In a vital decision that will helps (A)/ secure the rights of Internet users in country, (B)/ the Telecom Commission have approved the recommendations of the Telecom Regulatory Authority of India on net neutrality (C).
A) In a vital decision that will help secure
B) the rights of Internet users in the country,
C) the Telecom Commission have approved the recommendations of the Telecom Regulatory Authority of India on net neutrality.
1) A only   2) C only   3) A and B   4) B only 5) A and C

8. Union Minister Anantakumar Hegde apologized to the parliament (A)/ for his remarks last December that BJP had come to power (B)/ to changing Constitution (C).
A) Union Minister Anantakumar Hegde apologized to the parliament
B) for his remarks last December that BJP had come
C) to power to change the Constitution.
1) A only    2) A and B    3) B only    4) C only   5) B and C

9. Non-life insurers has pointed out to challenges in implementing the Supreme Court order (A)/ ask them to issue three year and five year insurance policies for four-wheeled and two-wheeled respectively. (B)/ Non-life insurers has recommended bifurcation the mandatory third party insurance cover (C).
A) Non -life insurers has pointed out to challenges in implementing
B) the Supreme Court order asking them to issue three year and five year insurance policies
C) for four-wheelers and two-wheelers respectively.
1) B only   2) C only   3) A only   4) A and C   5) B and C

10. Calls for data localisation is not new. (A)/ It has been a mainstay of Indian policymakers  demands from foreigner technology companies. (B)/ The Srikrishna Committee in its report note that eight of the top ten most accessed websites in India are owned by US entities (C).
A) Calls for data localisation are not new.
B) It has been a mainstay of Indian policymakers' demands from foreigner technology companies.
C) The Srikrishna Committee in its report note that eight of the top ten most accessed websites in India are owned by US entities.
1) A only    2) B and C   3) B only   4) C only   5) A and C

Directions (Q.11-20): Under each question a sentence is divided into five parts and numbered 1, 2, 3, 4,and 5. Your job is to identify the part which is GRAMMATICALLY wrong. If you think that the sentence is correct as it is, CHOOSE No error option(5) as your ANSWER. Some of the questions are taken from previous exams. 

11. Being (1)/ very dark (2)/ the visitors found it (3)/ difficult to locate the light switch (4)/. No error (5)/ 

12. It is high time (1)/ the Centre (2)/ clears (3)/ the Women Reservation Bill (4)/. No error (5)/

13. My parents (1)/ are leaving (2)/ to (3)/ the US next week (4)/. No error (5)/

14. The Vice Chancellor (1)/ of Delhi university (2)/ wants all vacancies (3)/ to be filled up soon (4)/. No error (5)/

15. Geeta and Sita (1)/ are sisters (2)/ and Sita is the tallest (3)/ of the two (4)/. No error (5)/ 

16. Veena went (1)/ America two times (2)/ in the past one year (3)/ for attending some international conventions (4)/. No error (5)/

17. Every boy (1)/ every girl (2)/ are to be given (3)/ a packet of sweets (4)/. No error (5)/

18. We must (1)/ always help (2)/ the poor (3)/ and needy (4)/. No error (5)/

19. The thieves (1)/ opened (2)/ the cash chest (3)/ by a screwdriver (4)/. No error (5)/

20. Many MPs (1)/ were caught (2)/ in the Parliament (3)/ watching porn on their mobiles (4)/. No error (5)/

Directions (Multiple - Error Q.21): Under the question, you find a sentence and the same is divided into FOUR PARTS and named A, B, C,and D. You have to identify the part or the parts that need some grammatical corrections and mark it/ them as your answer. If you think that the sentence is correct as it is, choose the option, "No Correction Required" (Option 5).

21. If Rani has a way with word, a good sense of design and administrative ability, she may enjoy working in the pressure world of advertising.
A) if Rani has a way with word
B) a good sense....ability
C) she may enjoy working
D) in the....advertising.
1) Only A   2) Only B   3) Only D   4) A and C   5) no correction required.

KEY

1-5,  2-2,  3-4, 4-5, 5-3, 6-5, 7-2, 8-2, 9-3, 10-2, 11-1, 

12-2, 13-3, 14-4, 15-3, 16-3, 17-3, 18-4, 19-4, 20-3, 21-5
 
 EXPLANATION

1. Use Nullify after to. It means to 'cancel' or 'damage'

2. The noun 'Row' has a couple of meanings. One meaning is a fight, a dispute. This singular noun takes the verb in singular.

3. The word 'Wrong' can be used as a Noun, a Verb, an Adjective and an Adverb. 'Wrongly' is also its another Adverbial form. Here the Adverb 'Wrong' means 'Unsuitable' and it modifies the verbs 'Think' and 'Do' in the sentence.

4. Here all the three statements are correct and so need no corrections.

5. The correct version is 'Committed itself to leave---' 'A less-welcome America'

6. The correct version is 'One reason Donald Trump inviting acres of commentary is that he keeps the world guessing what he means and where his foreign policy is heading for.'

7. The Subject is singular and it takes the verb, 'Has'

8. Do not use the Definite Article, 'The' before the word 'Parliament' and use always 'The' before the names of political parties.

9. Here the Subject 'Non-life insurers is plural and use the verb, 'Have'

10. In the B option it must be 'Foreign' not 'Foreigner' and in the C option it must be 'Notes'