Question

A number is increased by $20\%$ and then is decreased by $20\%$. Find the net increase or decrease percent?

Answer 1

Let the number $\left(N\right)$ be $100$

It is given that first the number is increased by $20\%$

So, New number $\left(N_1\right)=100+20\%$ of $100=100+0.2\times 100=100+20=120$
Also given that the increased number $\left(N_1\right)$ is decreased by $20\%$

So, New number after decrement $\left(N_2\right)=120-20\%$ of $120=120-0.20\times 120=96$

Change in original number $=96-100=-4$

Percentage change in original number $=\frac{\text{Change in original number}}{\text{Original number}}\times 100\%$

$=\frac{-4}{100}\times 100\%$

$=-4\%$

Hence, the original number will decrease by $4\%.$