Question

Arvind spends $75\%$ of his income. His income is increased by $20\%$. He increased his Expenditure by $10\%$. Find percentage increase in his saving.

• A. $80\%$
• B. $25\%$
• C. $75\%$
• D. $50\%$

Answer 1

The correct option is D $50\%$

Let initial income be $x$

Since Arvind spends $75\%ofx$

$\therefore expenditure=\frac{75}{100}\times x$

$=\frac{3x}{4}$

$\therefore savings=x-\frac{3x}{4}=\frac{x}{4}$

Increase in expenditure $=10\%$

$\therefore Newexpenditure=\frac{3x}{4}(1+\frac{10}{100})$

$=\frac{33x}{40}$

Increase in income$=20\%$

$\therefore Newincome=x(1+\frac{20}{100})$

$=\frac{6x}{5}$

Savings$=$New income$-$4New expenditure

$\frac{6x}{5}-\frac{33x}{40}=\frac{48x-33x}{40}$

$=\frac{3x}{8}$

Let percentage increase in saving be ${}^{\prime }{r}^{\prime }$

$\therefore \frac{x}{4}(1+\frac{r}{100})=\frac{3x}{8}$

$=>1+\frac{r}{100}=\frac{3}{2}$

$=>\frac{r}{100}=\frac{1}{2}$

$r=50\%$

$\therefore increaseinsavings=50\%$