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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%.
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