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.