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?

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

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

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

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

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

$\Rightarrow x=3$

 So, the can contained 21 litres of A.