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A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of the mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A were initially in the can?

1. 10
2. 20
3. 21
4. 25

Correct answer: 21

Solution

Initially, A and B are in the ratio 7:5, so their amounts are \(7x/12\) and \(5x/12\). After removing 9 litres, the remaining amounts are reduced in the same ratio, and then 9 litres of B are added. Using the final ratio 7:9 gives x = 36, so initial A = 7/12 of 36 = 21 litres.

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