Question

A number is increased by $15\%$ and then reduced by $15\%$. What is the effective increase or decrease in the original number?

• A. Doesn’t change
• B. Decreases by $2.25\%$
• C. Increases by $2.25\%$
• D. Increases by 2.75%

Answer 1

The correct option is B Decreases by $2.25\%$

Let the number be $x$
$15\%ofx=0.15x$
Given, the number $x$ is increased by $15\%$ .

Hence, the increased number
$=x+0.15x=1.15x$

$Now,15\%of1.15x=0.15\times 1.15x$
$=0.1725x$

$\text{Now, the number}1.15x\text{has to be}$
$\text{reduced by}15\%$

$Hence,thefinalreducednumber$
$=1.15x-0.1725x=0.9775x$


$\therefore$ Effective change
$=x-0.9775x$
$=0.225x$
$=2.25\%ofx$

Thus, the number is effectively decreased by 2.25%.