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

Quantity I. 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 .

Quantity II. A Can contains a mixture of two liquids A and B in the ratio 4:1. When 10 litres of mixture are drawn off and the Can is filled with B, the ratio of A and B becomes 2: 3

Solution

Quantity I. Suppose the Can initially contains 7x and 5x litres of mixtures A and B respectively.  Quantity of A in mixture left = (7x-7/12×9) = (7x-21/4) litres Quantity of B in mixture left = (5x-5/12×9) = (5x-15/4) litres ((7x-21/4))/((5x-15/4+9) ) = 7/9  ⇒ (28x – 21 )/(20x + 21) = 7/9 ⇒ 252x – 189 = 140x + 147   ⇒ x = 3. ∴ Quantity of A in the Can initially = 7 x = 21 Quantity II. Suppose the Can initially contains x and 4x litres of mixtures A and B respectively.  Quantity of A in mixture left = (4x-4/5×10) = (4x-8) litres Quantity of B in mixture left = (1x-1/5×10) = (1x-2) litres  ((4x-8))/((1x-2 +10)  ) = 2/3   ⇒ 12x – 24 = 2x + 16  ⇒ x = 4. ∴ Quantity of A in the Can initially = 4x = 16 Hence, Quantity I > Quantity II