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A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of 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 was contained by the can initially?

Correct Answer: 21

Explanation:

Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively

Quantity of A in mixture left = $7 x - \frac{7}{12} \times 9 = 7 x - \frac{21}{4}$ litres.

Quantity of B in mixture left = $5 x - \frac{5}{12} \times 9 = 5 x - \frac{15}{4}$ litres.

$\frac{7 x - \frac{21}{4}}{5 x - \frac{15}{4} + 9} = \frac{7}{9}$

$\Rightarrow \frac{28 x - 21}{20 x + 21} = \frac{7}{9}$

$\Rightarrow x = 3$

So, the can contained 21 litres of A.

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