How many litres of liquid A was contained by the can initially?

Question

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?

Answer 1

Initially, Liquid A = 21 litres
Say, initially amount of liquid A= X, and amount of liquid B = Y then,
X/(X+Y) = 7/12 => 12X= 7X+7Y => 5X=7Y
After drawing 9 litres of mixture and fillinf with 9 litre of liquid B;
(X-(7/12)(9))/(Y-(5/12)(9)+9) = 7/9
Solving, we get => (4X-21)/(4Y+21) = 7/9 => 36X-189=28Y+147 => 36X-28Y=336 => 9X-7Y = 84,
but, as we know, X=7Y/5, replacing we get => 9*7Y/5 - 7Y = 84 ==> 63Y-35Y = 420 ==> Y= 420/28 = 15
Hence, X=7*15/5 = 21