Question

If Mohan's income is $25\%$ more than Raman's income, then Raman's income is less than Mohan's income by

(a) $25\%$
(b) $80\%$
(c) $20\%$
(d) $75\%$

Answer 1

The correct option is (c): $20\%$

Let Raman's income be $x.$ It is given that Mohan's income is $25\%$ more than Raman's income.

Then, Mohan's income = $x+25\%$ of $x=x+\frac{25}{100}x=x(1+\frac{25}{100})$

$=x\left(\frac{100+25}{100}\right)=\frac{125}{100}x=\frac{5x}{4}$

$\therefore$ Raman's income as compared to Mohan's income (in $\%$)

$=\frac{\text{Mohan's income - Raman's income}}{\text{Mohan's income}}\times 100\%$

$=\frac{\frac{5x}{4}-x}{\frac{5x}{4}}\times 100\%=\frac{\left(\frac{5x-4x}{4}\right)}{\left(\frac{5x}{4}\right)}\times 100\%$

$=\frac{x}{5x}\times 100\%=20\%$