**Solved Examples**

**Example 1 :**

Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio must these metals be mixed. so that the mixture may be 12 times as heavy as water.

(1) 2:3 (2) 3:7 (3) 1:3 (4) 7:3 (5) None of these

**Sol. **(2)

Suppose Gold and Copper are taken in the ratio ‘X’ and ‘Y’, then

**Example 2 :**

Several liters of acid were drawn off from a 54 litre vessel full of acid and equal amount of water was added. Again the same volume of the mixture was drawn off and replaced by water. As result now, the vessel contained 24 litres of pure acid. How much of the acid was drawn off initially?

(1) 12 (2) 16 (3) 18 (4) 24 (5) None of these

**Sol.** (3)

Let a container contains ‘x’ units of liquid and ‘y’ units of liquid is taken out from it. If this operation is repeatable ‘n’ times. Then the final quantity of the liquid in the

**Example 3 :**

A fruit seller has 24 kg of apples. He sales a part of this at a gain of 20% and the balance at loss of 5 %. If on the whole earns a profit of 10 % the amount of apples sold at a loss is

(1) 9 kg (2) 9.6 kg (3) 10.5kg (4) 11kg (5) None of these

**Sol. **(2)

**Example 4 :**

‘3’ vessel whose capacities are in the ratio of 6 : 3 : 2 are completely filled with milk and water. The ratio of milk and water in the mixture 2:3. 4: 2 and 5 : 2. Taking _{} of first _{} of second and _{} of third. New mixture kept in new vessel. What is the percentage of water in the new mixture.

(1) 42% (2) _{} (3) 43% (4) 40% (5) None of these

**Sol.** (2)

**Example 5 :**

There is a mixture of alcohol and water containing 60% alcohol. Rahul wants to dilute the mixture to 50% by adding some quantity of water. He added pure alcohol to the mixture, now to get the mixture to 50% diluted. How much water as a fraction of the mixture must be added?

**Sol. **(3)

Initial quantity of mixture is ‘x’ and quantity of water required to the mixture diluted 50% is ‘y’,

Taking y = k and x = 5k, Quantity of mixture is ‘6k’. Quantity of alcohol is 4k.

**EXERCISE**

**1. **There are two vessels A and B. Vessel ‘A’ is containing 40 litres of pure milk and vessel ‘B’ containing 22 litres of pure water. From vessel A, 8 litres of milk is taken out and poured in to vessel ‘B’. Then 6 litres of mixture is taken out and from Vessel B poured into vessel A. What is the ratio of the quantity of pure milk in vessel ‘A’ to the quality of pure water in vessel ‘B’

**A: **21 : 11

**Sol.**

A = 40 (milk); B = 22 (water)

From question,

A = 40 – 8 = 32 litres; B = 8 litres (milk)

Mixture in vessel ‘B’ = 22 + 8 = 30 litres

**2. **A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy ‘C’, the ratio of gold and copper ‘C’ will be

**A:** 7 : 5

**Sol.**

**3. **Four vessels of equal sizes contain mixture of spirit and water. The concentration of spirit in 4 vessels are 60%, 70%, 80% respectively. If all the four mixtures are mixed. Find in the resultant mixture in the ratio spirit to water.

**A:** 57 : 23

**Sol.**

**4.** If 5 kg metal of which _{} is Zinc and the rest copper be mixed with 3 kg of metal of which _{} is Zinc and the rest copper, What is the ratio of Zinc to copper in the mixture.

**A:** 5 : 3

**Sol.**

Quantity of Zinc in the mixture

Quantity of copper in the metal = 5 + 3 – 5 = 3

.^{.}. Ratio = 5 : 3.

**5. **Two casks of 48 and 42 litres are filled with mixtures of wine and water, the proportions in the two casks being respectively 13 : 7 and 18 : 17. If the contents of the two casks be mixed and 20 litres of water added to the whole what will be the proportion of wine to water in the result?

**A: **12 : 13

**Sol.**

**6. **A man mixs ‘6’ litres of milk at Rs.650 per litre with 7 litres at Rs. 600 and with sufficient water to make the average value Rs. 540 per litre. How many litres of water has he added?

**A: **2

**Sol.**

Let water = x litre

Cost of ‘6’ litres of milk = 6 × 650 = 3900

Cost of ‘7’ litres of milk = 7 × 600 = 4200

Total amount of mixture = 7 + 6 + x = (13 + x) litres

Total cost of mixture = 3900 + 4200 = 8100

**7.** In on alloy, Zinc and copper are in the ratio 2 : 3. in the second alloy the same elements are in the ratio 4 : 5. In what ratio should these two alloys be mixed to form a new alloy in which the two elements are in the ratio 6 : 5?

**A:** 25 : 36

**Sol.**

**8.** Tejashwini purchased 160 kg of Rice at the rate of Rs. 25 per kg at a profit of 20%. At what rate per kg should she sell the remaining to get a profit of 30% on the total deal?

**A: **34

**Sol.**

S.P of kg at 20% profit on ‘25’ = Rs. 30

S.P per at 30% profit on ‘25’ = Rs. 32.5

Ratio of kg = 60 : 100 = 3 : 5

**9. **A container contains 8 parts of milk and 4 parts water. How many parts of mixture should be taken out and replaced by water so that container contains half milk and half water.

**A:**

**Sol. **

_{}

**10. **How much water must be added to a cask containing 40 litres of spirit worth Rs. 15.68 litre to reduce the price to Rs. 12.96 a litre?

**A: **8_{}

**Sol.**

**11.** One type of liquid contains 12_{}% of milk the other contains 15% of milk. A can is filled with 8 parts of the first liquid and 12 parts of the second liquid. Find the percentage of milk in the new mixture.

(1) 12% (2) 13% (3) 15% (4) 14% (5) None of these

**A:** 5(None of these)

**Sol.**

**12.** Weights of two friends Prem and Kalyan are in the ratio of 2 : 3 Prem’s weight increases by

6_{} and the weight of Prem & Kalyan together become 41kg, with an increase of 8%. By what percent did the weight of Kalyan increase?

**A: **9%

**Sol.**

**13. **An 25litres cylinder contains a mixture of oxyzen and nitrozen, the volume of oxyzen being 25% of total volume. A few litres of the mixture is released and an equal amount of nitrozen is added. Then the same amount of mixture as before is released and replaced by nitrozen for the second time. As a result, the oxyzen content becomes 9% of the total volume. How many litres of mixture released each time.

**A:** 10 lit

**Sol.**

**14. **A vessel contains 125 litres of wine. 25 litres of wine was taken out of the vessel and replaced by water. Then 25 litres of mixture was withdrawn and again replaced by water. The operation was repeated for 3rd time. How much time wine is now left the vessel.

**A: **64

**Sol.**

**15. **19 litres drawn from a vessel full of spirit and filled with water. Then 19 litres of mixture are drawn and the vessel is again filled with water. The ratio of the spirit to water now present in the vessel is 81:19. What is the full capacity of the vessel.

**A: **190

**Sol.**