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?

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

Answer 1

Answer: (C)

$21$

Suppose the can initially contains $7x$ and $5x$ of mixtures $A$ and $B$ respectively.
Quantity of $A$ in mixture left $=(7x-\frac{7}{12}\times 9)$ litres $=(7x-\frac{21}{4})$ litres.
Quantity of $B$ in mixture left $=(5x-\frac{5}{12}\times 9)$ litres $=(5x-\frac{15}{4})$ litres.
$\therefore \frac{(7x-\frac{21}{4})}{(5x-\frac{15}{4})+9}=\frac{7}{9}$
$\Rightarrow \frac{28x-21}{20x+21}=\frac{7}{9}$
$\Rightarrow 252x-189=140x+147$
$\Rightarrow 112x=336$
$\Rightarrow x=3$.
So, the can contained $21$ litres of $A$.