Question

A plastic 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. Initially quantity of liquid A in the mixture is ___ liter(s).

Answer 1

Suppose the can initially contains 7x and 5x litre of liquid A and B in the mixture respectively.
Quantity of A in mixture left = $7x-\frac{7}{12}\times 9=(7x-\frac{21}{4})l$
Quantity of B in mixture left = $5x-\frac{5}{12}\times 9=(5x-\frac{15}{4})l$
Also, 9 litre of B is added
Quantity of B will be = $(5x-\frac{15}{4}+9)l$
Now, $\frac{7x-\frac{21}{4}}{5x-\frac{15}{4}+9}=\frac{7}{9}\frac{28x-21}{20x+21}=\frac{7}{9}x=3$
So, the can contained 21 litres of liquid A.