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An 84-litre mixture contains milk and water in the ratio $5:2$. After removing 21 litres of the mixture, 12 litres of pure milk is added. What is the new ratio of milk to water?

1. 13:8
2. 27:14
3. 19:6
4. 21:11

Correct answer: 19:6

Solution

The 84-litre mixture in the ratio $5:2$ has milk $=60$ litres and water $=24$ litres. Removing 21 litres removes milk and water in the same ratio, so 15 litres milk and 6 litres water are removed; then 12 litres of milk is added. Thus milk becomes 57 litres and water remains 18 litres, giving the ratio $57:18=19:6$.

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