Question

A can contains a mixture of two liquids $A$ and $B$ in the ratio $3:4.$ When $14$ litres of mixture are drawn off and the can is filled with $A,$ the ratio of $A$ and $B$ becomes $3:2.$ How many litres of liquid $A$ was contained by the can initially?

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

Answer 1

The correct option is B $20$

Suppose the can initially contains $3x$ litres and $4x$ litres of liquids $A$ and $B$ respectively.
After drawing off $14$ litres of mixture,
Quantity of $A$ left in mixture $=(3x-\frac{3}{7}\times 14)=(3x-6)$ litres
Quantity of $B$ left in mixture $=(4x-\frac{4}{7}\times 14)=(4x-8)$ litres

According to question,
$\frac{(3x-6)+14}{4x-8}=\frac{3}{2}$
$\Rightarrow \frac{3x+8}{4x-8}=\frac{3}{2}$
$\Rightarrow 6x+16=12x-24$
$\Rightarrow 6x=40$
$\Rightarrow x=\frac{20}{3}$
$\Rightarrow 3x=20$
So, the can contained $20$ litres of liquid $A.$