Question

A tin contains a mixture of two liquids $A$ and $B$ in the proportion $4:1.$ If $45$ litres of the mixture is replaced by $45$ litres of liquid $B,$ the ratio of the two liquids becomes $2:5.$ Then in the new mixture, the quantity of liquid $B$ is

• A. $50$ litres
• B. $42$ litres
• C. $56$ litres
• D. $62$ litres

Answer 1

The correct option is A $50$ litres

Let the quantity of $A$ and $B$ be $4k$ and $k$ in the previous mixture.
After removing $45$ litres of mixture,
quantity of $A=4k-\frac{4}{5}\times 45=4k-36$
quantity of $B=k-\frac{1}{5}\times 45=k-9$

Now, $45$ litres of liquid $B$ is added.
Then, quantity of $B=k-9+45=k+36$

Now, ratio of quantity of $A$ and $B$ is $\frac{4k-36}{k+36}=\frac{2}{5}$
$\Rightarrow 20k-36\times 5=2k+36\times 2$
$\Rightarrow 18k=36\times 7$
$\Rightarrow k=14$

Quantity of liquid $B$ in new mixture $=k+36=14+36=50$ litres