# Q. There are two containers X and Y. X contains 100 ml of milk and y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

a. m = n

b. m>n

c. m < n

d. Cannot be determined due to insufficient data

Correct Answer: a. m = n

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation : **

## There are two containers X and Y

X contains 100 ml of milk. Y containes 100 ml of water.

20 ml of milk from X is transferred to Y.

Now, we get,

X → Milk = 80 ml

Y → Milk = 20 ml and Water = 100 ml

Total mixture in Y is 120 ml in which ratio of Milk and Water is 1 :5 respectively.

After that 20 ml of the mixture of Y is transferred to X,

Mixture to be transferred from Y = Y → Milk = 20/6, Water = (20/6) × 5 = 100/6

Remaining mixture in Y = Y → Milk = 20 – (20/6) = 100/6, Water = 100 – (100/6) = 500/6

New Mixture in X = X → Milk = 80 + (20/6) = 500/6, Water = 100/6

It is given that m denotes the proportion of milk in X i.e. 500/6

It is given that n denotes the proportion of water in Y i.e. 500/6

It means m = n.