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

$20\%$

Step 1: Solve for the difference between Mohan's and Raman's income.

Let us assume Mohan's income be $X$and Raman's income be $Y$

Given that,

Mohan's income is $25\%$ more than Raman's income i.e. $X=Y+25\%ofY$

$X=Y+\left(\frac{25}{100}\right)Y$

$X=Y\left(1+\left(\frac{25}{100}\right)\right)$

$$\begin{gathered} X=Y\left(\frac{\left(100+25\right)}{100}\right) \\ X=Y\left(\frac{125}{100}\right) \end{gathered}$$

Then the difference between both the income is $=\left(\frac{125}{100}\right)Y-Y=\frac{25}{100}Y$

Step 2: Solve for Raman's income in comparison to Mohan's income.

Raman's income as compared to Mohan's income $=\frac{\left(Difference\right)}{(Mohan\text{'}sincome)}\times 100$

$$\begin{gathered} =\left(\frac{\left({\displaystyle \frac{25Y}{100}}\right)}{\left({\displaystyle \frac{125Y}{100}}\right)}\right)\times 100 \\ =\left(\frac{25}{125}\right)\times 100 \\ =20\% \end{gathered}$$

Raman's income is $20\%$less than Mohan's income.

Hence, the correct option is option (C) i.e. $20\%$