A Cistern contains a mixture of two liquids A and B in the ratio of 7 : 5, when 9 liter of mixture is drawn off and replaced with B then the ratio of A and B becomes 7 : 9.  Find the quantity of A initially. 

21

Method one:

The ratio   A   :   B

                7   :   5

So, the answer will be in the multiple of (7). Therefore, 21 liters is the answer.

Method two:

               A   :   B

               7   :   5

                        ↓+4R = 9 ltrs

               7   :   9

1R = \(\frac{9}{4}\)

Final Qty. 16R  = \(\frac{9}{4}\) × 16 = 36 liters = Initial Qty.

Initial ratio = 7   :   5   =    12

12R = 36

1R = 3

Qty. of A initially = 7R = 3 × 7 = 21 liters