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A mixture containing 60 litres contains milk and water in the ratio 3:2. If one-third of 50% of the mixture is withdrawn and replaced with \(x\) litres of water, and the quantity of water in the container becomes 10 litres more than the milk, find the value of \(x\).

1. 35
2. 40
3. 20
4. 25

Correct answer: 20

Solution

Initially, milk = 36 litres and water = 24 litres. One-third of 50% of 60 litres means 10 litres of mixture is withdrawn, so 6 litres milk and 4 litres water are removed. Remaining milk = 30 litres and water = 20 litres; after adding \(x\) litres of water, water becomes \(20 + x\). Since water is 10 litres more than milk, \(20 + x = 30 + 10\), giving \(x = 20\).

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