A bucket contains a mixture of two liquids A and B in the proportion 7: 5 . If 9 litres of the mixture is replaced by 9 litres of liquid B, then the ratio of the two liquid becomes 7: 9. How much of the liquid A was there in the bucket?

Initial mixture has A:B = 7:5. When 9 litres of mixture is removed, the amount of A removed is (7/12)×9 = 21/4 litres. If initial total is 12k litres, then A remaining is 7k - 21/4. After adding 9 litres of B, new total is still 12k litres with new ratio A:B = 7:9. Therefore, (7k - 21/4)/(5k + 21/4) = 7/9. Solving gives k = 3, so initial A = 7×3 = 21 litres.