The salary of an officer is increased by 25%.

Question:

The salary of an officer is increased by 25%. By what per cent should the new salary be decreased to restore the original salary?

Solution:

Let the original salary be Rs 100

Then, after increment of 25% the salary becomes

$=100\left(1+\frac{25}{100}\right)=100\left(\frac{125}{100}\right)=R s 125$

To restore the original salary, let the new salary be decreased by x%.

Thus, we get

$125\left(1-\frac{x}{100}\right)=100$

$\Rightarrow\left(1-\frac{x}{100}\right)=\frac{100}{125}=\frac{4}{5}$

$\Rightarrow \frac{x}{100}=\frac{1}{5}$

$\Rightarrow x=\frac{100}{5}=20 \%$

Therefore, the new salary must be reduced by 20% to restore the original salary.

 

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