Question

A tank contains a mixture of two liquids $P$ and $Q$ in the ratio $1:2.$ When $9$ litres of mixture are drawn off and the tank is filled with $P,$ the ratio of $P$ and $Q$ becomes $3:2.$ How many litres of liquid $Q$ was contained by the tank initially?

• A. $15$ litres
• B. $10$ litres
• C. $12$ litres
• D. $18$ litres

Answer 1

The correct option is A $15$ litres

Suppose the tank initially contains $x$ litres and $2x$ litres of liquids $P$ and $Q$ respectively.
After drawing off $9$ litres of mixture,
Quantity of $P$ left in mixture $=(x-\frac{1}{3}\times 9)=(x-3)$ litres
Quantity of $Q$ left in mixture $=(2x-\frac{2}{3}\times 9)=(2x-6)$ litres

According to question,
$\frac{(x-3)+9}{2x-6}=\frac{3}{2}$
$\Rightarrow \frac{x+6}{2x-6}=\frac{3}{2}$
$\Rightarrow x+6=3x-9$
$\Rightarrow 2x=15$
So, the tank contained $15$ litres of liquid $Q.$