1. A milkman has a mixture of 280 l, which contains milk and water in the ratio 5 : 2. Milkman sold 84 l of the mixture and mixed milk and water in the ratio of 3 : 1 in remain mixture. If the ratio of milk to water in the final mixture is 44 : 17, then find the water percentage in the final mixture.
2. A drum contains a mixture of two liquids, P and Q is in the respective ratio 5 : 3. When 20 liters of mixture are drawn off and the drum is filled with Q, the ratio of P and Q becomes 1 : 1. How many liters of liquid P was contained by the drum initially?
A) 60 l B) 62.5 l C) 72 l D) 65.5 l E) 78 l
3. A mixture of two containers, P and Q of equal capacity containing wine and water in the ratio 5 : 4, and 3 : 7, respectively, are poured into another vessel R. If the water in vessel R is 103 litres, then find the initial quantity of wine in vessel P.
A) 100 B) 80 C) 75 D) 66 E) 50
Explanation:
Container - P Container - Q
wine : wate wine : water
5 : 4 3 : 7
equating the quantity of containers P & Q
(5 : 4) × 10 (3 : 7) × 9
30 : 40 27 : 63
Water quantity in R = 103 l
then initial quantity of wine in P = 50 l
Ans: E
4. 20 liters of pure water was added to a vessel containing 80 liters of pure milk. 25 liters of the resultant mixture was sold and some more quantity of pure milk and pure water was added to the vessel in the respective ratio of 2 : 1. If the resultant respective ratio of milk and water in the vessel 3 : 1, what was the quantity of pure water added in the vessel?
A) 17 B) 20 C) 15 D) 12 E) 24
Explanation: Milk : Water
80 l : 20 l
Milk & Water all in the ratio 4 : 1
25 letters mixture was sold the ratio of 4 : 1
60 + 2x = 45 + 3x
x = 15
Quantity of pure water added in the vessel = 1x = 15 l
Ans: C
5. Two jars contain a mixture of milk and water. The first jar contains 65% milk and second jar contains 25% water. In what ratio these two mixtures are mixed so that the new mixture contains 67% milk?
A) 1 : 2 B) 3 : 8 C) 4 : 1 D) 5 : 9 E) 2 : 9
Explanation: First jar milk = 65%
second jar milk =100 − 25% = 75%
Ans: C
6. 162 litres of a mixture of ethanol and water, the ratio of ethanol to water is 8 : 7, if 18 litres mixture taken out from the mixture, and the same amount of water added in the mixture then find the percentage of ethanol in the new mixture found? (approximately)
A) 47.2 B) 52.3 C) 41.6 D) 56.9 E) 45.6
7. A container contains 275 litres of orange juice. Some quantity of orange juice is taken out and water added in the container which is equal to one-third of that quantity of orange juice taken out in the container. Respective ratio of water to orange juice in the container becomes 8 : 31. What is the quantity of water added in it?
A) 60 B) 28 C) 32 D) 45 E) 40
6600 − 24x = 31x ⇒ 55x = 6600 ⇒ x = 120
Quantity of water added in the vessel
Ans: E
8. A container contains a mixture of milk and water in the ratio 7 : x. If 20 litre of water is added to the mixture, then the ratio of milk to water becomes 7 : 15 and if 10 litres of water is added then the ratio of milk to water becomes 14 : 25. Find the quantity of milk in the initial mixture
A) 24 B) 40 C) 28 D) 32 E) 66
Explanation: milk : water
7y : xy
175y = 14xy + 140 .......... (2)
solving 1& 2
y = 4
Initial quantity of milk in mixture 7y = 7 × 4 = 28 l
Ans: C
9. A container contains 675 liters mixture of milk & water in the ratio of 13 : 14. If X liters of mixture taken out and (X − 6) liters of milk & (X − 28) liters of water added in remaining mixture so the ratio of milk & water becomes equal. Find quantity of milk in original mixture is what percent of total final mixture? (Approximately)
A) 45% B) 28% C) 23.5% D) 36% E) 52%
10. Milk container contains 50 liters of milk. If ‘x’ liters of milk is taken out and replaced by water, this process is repeated two more times and then the quantity of the water in the container is 24.4 liters, find the value of x.
A) 8 B) 10 C) 9.4 D) 8.6 E) 9
(50 − x)3 = 64000
(50 − x)3 = (40)3
50 − x = 40
50 − x − 40 ⇒ x = 10
Ans: B
11. A container contains 171 l mixture of whisky and soda in the ratio 10 : 9 respectively. 95 litres of the mixture used in a party and 9 litres pure whisky and 6 litres soda added to the container. Find the ratio between the quantity of whisky and quantity of soda in the final mixture.
A) 7 : 6 B) 5 : 4 C) 9 : 7 D) 3 : 2 E) 6 : 7
Ans: A
