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 $A$ and $B$ becomes $7:9$. How many litres of liquid $A$ was contained by the can initially ?

• A. $10$
• B. $20$
• C. $21$
• D. $25$

Answer 1

Answer: (C)

$21$

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

Quantity of A in mixture left$=(7x-\frac{7}{12}\times 9)=(7x-\frac{21}{4})$ litres

Quantity of B in mixture left $=(5x-\frac{5}{12}\times 9)=(5x-\frac{15}{4})$ litres

Now,

$\frac{7x-\frac{21}{4}}{5x-\frac{15}{4}+9}=\frac{7}{9}$

$=>\frac{28x-21}{20x+21}=\frac{7}{9}$

$=>252x-189=140x+147$

$=>x=3$

Thus, the can contains $21$ litres of $A$.