Question

Ratio of income of $A$ and $B$ is $6:5$ ratio of their expenditure is $3:2$, if $A$ saves ${\frac{1}{4}}^{\left(th\right)}$ of his income , find ratio of their monthly savings?

• A. $1:2$
• B. $2:3$
• C. $3:4$
• D. $4:5$

Answer 1

The correct option is C $3:4$

Let the income of $A=6x$

Let the income of $B=5x$

Let the expenditure of $A=3y$

Let the expenditure of $B=2y$

Therefore , savings of $A=6x-3y$

Savings of $B=5x-2y$

Now, as $A$ saves ${\frac{1}{4}}^{th}$ of his income,

$6x-3y=\frac{1}{4}\left(6x\right)$

$24x-12y=6x$

$18x=12y$

$3x=2y$

Now, ratio of savings of $A$ and $B$ $=\frac{6x-3y}{5x-2y}$

$=\frac{6x-\left(\frac{3}{2}x\right)\times 3}{5x-3x}=\frac{3}{4}=3:4$