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A 40-litre mixture of acid and water contains acid and water in the ratio 3:1. Eight litres of this mixture is removed and replaced with another solution of acid and water in the ratio 1:3. What is the final ratio of acid to water in the resulting mixture?

1. 1:1
2. 13:7
3. 13:5
4. 5:3

Correct answer: 13:7

Solution

Initially, acid = 30 L and water = 10 L. Removing 8 L of a 3:1 mixture removes 6 L acid and 2 L water, leaving 24 L acid and 8 L water. Replacing with 8 L of a 1:3 mixture adds 2 L acid and 6 L water, giving 26 L acid and 14 L water, i.e. 13:7.

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