Question

The ratio of petrol and kerosene in the container is $3:2$, when $10$ litre of the mixture is taken out and is replaced by the kerosene, the ratio become $2:3$ Then the total quantity of the mixture in the container is ___

Answer 1

Suppose, Initially petrol and kerosene be $3x$ and $2x$ litres respectively.
When $10$ litres of mixture is taken out from the mixture.
Quantity of petrol left in the mixture $=3x-\frac{3}{5}\times 10$
$=(3x-6)$ litres
Quantity of kerosene left in the mixture $=2x-\frac{2}{5}\times 10$
$=(2x-4)$ litres
Also, $10$ litres of kerosene is added
Quantity of kerosene will be $(2x-4+10)=(2x+6)$ litres

Now, $\frac{3x-6}{2x+6}=\frac{2}{3}$
$\Rightarrow 3\times (3x-6)=2(2x+6)$
$\Rightarrow 9x-18=4x+12$
$\Rightarrow 5x=30$
$\Rightarrow x=\frac{30}{5}=6$

Quantity of petrol$=3x=3\times 6=18$ litres

Quantity of kerosene$=2x=2\times 6=12$ litres
Total, quantity of mixtures $=(18+12)=30$ litres