Question

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

Answer 1

Let $x$ be the number.

Increase in the number $=20\%ofx$

$=\frac{20}{100}\times x$

$=\frac{1}{5}\times x=\frac{x}{5}$

Increased number$=x+\frac{x}{5}$

$=\frac{5x+x}{5}=\frac{6x}{5}$

The resulting number decreased by $20\%$

Decrease in the number $=20\%of\frac{6x}{5}$

$=\frac{1}{5}\times \frac{6x}{5}=\frac{6x}{25}$

New number $=\frac{6x}{5}-\frac{6x}{25}$

$=\frac{30x-6x}{25}$

$=\frac{24x}{25}$

The net decrease $=x-\frac{24x}{25}$

$=\frac{25x-24x}{25}=\frac{x}{25}$

Net % decrease $=\frac{{\displaystyle \frac{x}{25}}}{x}\times 100$

$=\frac{x}{25}\times \frac{1}{x}\times 100=4\%$

Hence, the net percent decrease $=4\%$.