Ratio Proportion Mixtures Alligation

A can contains a mixture of two liquids A and B is 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?

  1. 10
  2. 20
  3. 21
  4. 25

Answer

Let can contains 7x and 5x of A and B respectively.

So, total volume = 12x

When 9 litres of mixture is removed, ((7/12) * 9) litres of A is removed, and ((5/12) * 9) litres of B is removed. Then 9 litres of B is added so that new ratio is 7:9.

In new mixture, total volume of A is 7x - ((7/12) * 9) = 7x - 21/4 

Total volume of B is 5x - ((5/12) * 9) + 9 = 5x - 3 3/4 + 9 = 5x + 21/4

So, (7x - 21/4)/(5x + 21/4) = 7/9

x = 3

Original Volume of A = 7x = 21

The correct option is C.