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A shopkeeper first increased the price of an article by 25% and then by 20%. What is the total percent increased?
Given:
A shopkeeper first increased the price of an article by 25% and then by 20%.
To do:
We have to find the total percent increased.
Solution:
Let the price of the article be $x$.
The price of the article after it is increased by 25%$=x+\frac{25}{100}x$
$=\frac{100x+25x}{100}$
$=\frac{125x}{100}$
$=\frac{5x}{4}$
The price of the article after it is increased by 20%$=\frac{5x}{4}+\frac{20}{100}\times\frac{5x}{4}$
$=\frac{5x}{4}+\frac{x}{4}$
$=\frac{5x+x}{4}$
$=\frac{6x}{4}$
$=\frac{3x}{2}$
The total percentage increase in the price $=\frac{\frac{3x}{2}-x}{x}\times100$%
$=\frac{\frac{3x-2x}{2}}{x}\times100$%
$=\frac{x}{2x}\times100$%
$=50$%
The total percent increased is 50%.
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