Question

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

Answer 1

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

$25\%ofn=n\times \frac{25}{100}$

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

Now, the value of 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
$=n\times \frac{5}{4}$ - $n\times \frac{1}{4}=\frac{5n-n}{4}=\frac{4n}{4}=n$

Net percent change
$=\frac{\text{amount changed}}{\text{original value}}\times 100$

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