A number was increased by 20% and then decreased by 20%. The net increase or decrease percentage is

Given:

A number was increased by 20% and then decreased by 20%. 

To do:

We have to find the net increase or decrease percentage.

Solution:

Let the number be $x$.

The number after it is increased by 20%$=x+\frac{20}{100}x$

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

$=\frac{120x}{100}$

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

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

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

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

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

The net decrease percentage $=\frac{x-\frac{24x}{25}}{x}\times100$%

$=\frac{x}{25x}\times100$%

$=4$%

The total percentage decreased is 4%.

Tutorialspoint

Updated on: 10-Oct-2022

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