A can contains a mixture of two liquids A and B in the ratio 5 : 3. When 12 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 5 : 8. How many litres of liquid A was contained by the can initially?

Question: A can contains a mixture of two liquids A and B in the ratio 5 : 3. When 12 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 5 : 8. How many litres of liquid A was contained by the can initially?

Solution:
Let liquids A is initially 5x, liquid B is 3x litres
12 litres of mixture are drawn, remaining mixture A = 5x - (5/8) × 12 = 5x - 7.5
Remaining mixture B = 3x - (3/8) × 12 = 3x - 4.5
After filling, mixture becomes = 3x - 4.5 + 12 = 3x + 7.5
5x - 7.5/3x + 7.5 = 5/8
⇒ (40x - 60)/(24x + 60) = 5/8
⇒ 320x - 480 = 120x + 300
⇒ 200x = 780
⇒ x = 3.9
Liquid A is (5 × 3.9) or 19.5 litres