Question

A jar is filled with a mixture of two liquids $A$ and $B$ in the proportion $A:B::5:3,$ when $16$ litres of the mixture is drawn off and the jar is filled with liquid $B,$ then the proportion becomes $A:B::3:5.$ How many litres of mixture does the jar hold?

• A. $35$ $L$
• B. $50$ $L$
• C. $45$ $L$
• D. $40$ $L$

Answer 1

The correct option is D $40$ $L$

Let the initial mixture of A be $5x$ and that of B be $3x$.

If 16L of the mixture was drawn, then the amount of A drawn is $16\times \frac{5}{8}$ which is $10L$

And that of B will be $16\times \frac{3}{8}$ which is $6L$.

The quantity of A left in the mixture is $(5x-10)$ and that of B will be $(3x-6)$.

The quantity of A and B after $16$ L was removed and being added with B,

$(5x-10)$ and $(3x-6)+16$.

The new ratio, is $\frac{5x-10}{3x-6+16}=\frac{3}{5}$

$\Rightarrow \frac{5x-10}{3x+10}=\frac{3}{5}\Rightarrow 25x-50=9x+30\Rightarrow 16x=80\Rightarrow x=5$

So, A contains $25$L and B contains $15$L. The total capacity of the jar is $40$ L.