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 - (7/12) × 9} = 7x - 21/4
Quantity of B in mixture left = {5x - (5/12) × 9} = 5x - 15/4

According to the question,
(7x - 21/4)/{(5x - 15/4) + 9} = 7/9
⇒ (28x - 21)/(20x + 21) = 7/9
⇒ 252x - 189 = 140x + 147
⇒ 252x - 140x = 147 + 189
⇒ 112x = 336
⇒ x = 3.

So, they can contain 21 litres of A.