Question

A number ‘n’ is first increased by 25% and then it is decreased by 20%. What is the net percentage change in the value of n?

Answer 1

The number 'n' is first increased by 25$\%$.

So, the new value of n
$=n+n\times \frac{25}{100}=n\times \frac{5}{4}$

Now, the value of 'n' is again decreased by $20$%.

So, $20$% of the new value
$=n\times \frac{5}{4}\times \frac{20}{100}=n\times \frac{1}{4}$

So, the new value
$=n\times \frac{5}{4}$ - $n\times \frac{1}{4}=n$

Net percent change
$=\frac{\text{Change in value}}{\text{Original value}}\times 100$

Net change = n - n = 0
So, on substituting the values, we get:
Net percent change = $\frac{0}{n}\times 100$ = 0
So, there is no percentage change.