A can contains a mixture of two liquid A and B in the ratio 7 : 5 when 9 liters of mixture are drown off and the can is filled with B ,the ratio of A and B becomes 7 : 9. how many liters of liquid A was contained by the can initialy.

Let the mixture of A = 7x

mixture of B = 5x

Remaining mixture of A = 7x - (7 / 12) * 9 = 7x - 63 / 12

Remaining mixture of B = 5x - (5 / 12) * 9 = 5x - 45 / 12

Add 9 liters in mixture of B = [5x - 45 / 12] + 9

A:B = 7 : 9

[7x - 63 / 12] / [5x - 45 / 12] + 9 = 7 / 9

(84x - 63) / (60x - 45 + 108) = 7 / 9

(84x - 63) / (60x + 63) = 7 / 9

756x - 567 = 420x + 441

336x = 1008

x = 3

Mixture of A = 7x = 7 * 3 = 21

21 liters of liquid A was contained by the can initialy.