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A mixture contains milk and water in the ratio 4:1. On adding another mixture containing 20 litres of milk and 10 litres of water, the new ratio of water to milk becomes 1:3. Find the difference in the quantities of milk and water in the initial mixture.

1. 10
2. 20
3. 30
4. 40

Correct answer: 30

Solution

If the initial mixture is 4x litres milk and x litres water, then after adding 20 litres milk and 10 litres water, the final ratio water:milk becomes 1:3. Solving gives x = 10, so the initial difference between milk and water is 4x - x = 3x = 30 litres.

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