Question

A can contains a mixture of two liquids a and b in 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 ?

Answer 1

Suppose the can initially contains 7x and 5x of mixtures A and B respectively.

Quantity of A in mixture left =7x -7x 9litres =7x -21 litres.124

Quantity of B in mixture left =5x -5x 9litres =5x -15 litres.124

7x -214=75x -15 + 949

28x - 21=720x + 219

 252x - 189 = 140x + 147

 112x = 336

 x = 3.

So, the can contained 21 litres of A.

Answer 2

Let us consider that the can Contains 7x and 5x of mixtures A and B Respectively 

Amount of A remained in mixture =   7x - 7/12 x 9 = (7x - 21 /4 )L 

Amount of B remained in mixture =   5x - 5/12 x 9 = (5x - 15 /4 )L 

After can is filled with B ....

(5x - 15/4)L + 9 L 

later required ratio

(7x - 21/4) / (5x - 15 / 4) + 9 

i.e. 7/9 = (7x - 21 /4) / (5x - 15/4) + 9 

252 x  - 189 =  140x + 147 

112x =  336 

x       = 3 

Now quantity of A = 7x = 7 x 3 = 21 L