A number is increased by 25% and the resulting number is then decreased by 20%. The final number is what percent of the original number?

I know the answer is 100 but how do I show it?

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- Mar 12th 2010, 02:31 AMdonnagirlPercents
A number is increased by 25% and the resulting number is then decreased by 20%. The final number is what percent of the original number?

I know the answer is 100 but how do I show it? - Mar 12th 2010, 02:54 AMSudharaka
Dear donnagirl,

Suppose your number is x, then when it is increased by 25% the resulting number is,

$\displaystyle x+\frac{25x}{100}$

Then the result is decreased by 20% that is,

$\displaystyle \left(x+\frac{25x}{100}\right)-\frac{20}{100}\left(x+\frac{25x}{100}\right)=\frac {5x}{4}-\frac{1}{5}\left(\frac{5x}{4}\right)=x$

So the number is 100% of the original number.

Hope this will help you.