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A vessel has 200 litres of milk and 40 litres of water. If _____ litres of mixture is taken from the vessel and _____ litres of water is added to the remaining mixture, then the final amount of milk in the vessel becomes 125 litres more than the amount of water in it. Which of the following integral values given in the options are possible in the blanks in the same order?

1. (a) only A
2. (b) only A, B and E
3. (c) only A and B
4. (d) only A, B and D
5. (e) All four are possible

Correct answer: (d) only A, B and D

Solution

The initial ratio of milk to water is 200:40 = 5:1, so any removed mixture has milk and water in the same ratio. After removing x litres and adding y litres of water, the final difference between milk and water must be 125 litres. Substituting each pair shows that only A, B and D satisfy the condition.

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