A bucket contains 2 mixtures A and B in the ratio 7:5. If 9 liters of the mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7:9. How much of the liquid A was there in the bucket?  Choose the correct choice from the following answers
A) 15 liters
B) 21 liters
C) 12 liters
D) 18 liters
E) 25 liters

Rationale: 1 st ratio = 7 : 5 2 nd ratio = 7 : 9 difference of cross products ratio = 7 * 9 - 7 * 5 = 28 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 9 / 7 + 5 ) + ( 9 * 7 / 28 ) = 3 quantity of a = 7 * 3 = 21 liters answer is b
Answer: B