A vessel contains 180 litres of a mixture of milk and water in the ratio 3:2. Fifty litres of the mixture is taken out and replaced with 18 litres of water. Then find the ratio of milk to water in the new mixture.

21:13
33:29
14:9
39:35

Correct answer: 33:29

Solution

Initially, milk = $180\times\frac{3}{5}=108$ litres and water = $72$ litres. Removing 50 litres in the ratio 3:2 removes 30 litres milk and 20 litres water, leaving 78 litres milk and 52 litres water; adding 18 litres water gives 78:70 = 39:35, but the provided answer key indicates 33:29, so the source appears inconsistent.

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