Question

Two liquids $A$ and $B$ are in the ratio $5:1$ in container 1 and $1:3$ in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of $A$ and $B$ in the ratio $1:1$?

• A. $2:3$
• B. $4:3$
• C. $3:2$
• D. $3:4$

Answer 1

The correct option is D $3:4$

Let the required ratio be x:y
Liquid A in x litres of mixture in container 1 $=\frac{5x}{6}$ litres

Liquid B in x litres of mixture in container 1 $=\frac{x}{6}$ litres

Liquid A in y litres of mixture in container 2 $=\frac{y}{4}$ litres

Liquid B in y litres of mixture in container 2 $=\frac{3y}{4}$ litres

$\therefore$ Liquid A: Liquid B = $[\frac{5x}{6}+\frac{y}{4}]:[\frac{x}{6}+\frac{3y}{4}]$

Given, $\frac{\frac{5x}{6}+\frac{y}{4}}{\frac{x}{6}+\frac{3y}{4}}=\frac{1}{1}\Rightarrow \frac{5x}{6}+\frac{y}{4}=\frac{x}{6}+\frac{3y}{4}\Rightarrow \frac{5x}{6}-\frac{x}{6}=\frac{3y}{4}-\frac{y}{4}\Rightarrow \frac{4x}{6}=\frac{2y}{4}\Rightarrow \frac{2x}{3}=\frac{y}{2}\Rightarrow \frac{x}{y}=\frac{3}{4}$