Question

A number is increased by $20$ and then decreased by $20$. Find the net increased or decreased per cent?

Answer 1

Let x be the number

The number after being increased by 20% $=x+\frac{20}{100}\times x.$

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

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

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

The new number decreased by 20 % $=\frac{6x}{5}-\frac{20}{100}\times \frac{6}{5}x$

$=\frac{6x}{5}-\frac{1}{5}\frac{6}{5}x$

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

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

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

$\therefore$ the new number $\frac{24x}{25.}$

decreased in percentage$=\frac{x-\frac{24}{25}}{x}\times 100$%

$=\frac{25x-24x}{25x}\times 100$ %

$=\frac{x}{25x}\times 100$% = 40%