Question

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

Answer 1

HINT: The formula for finding x percentage of any quantity 1 is
\[\dfrac{x}{100}\times Quantity\ 1\]

Complete step by step answer:
As per the question, the salary of an officer is increased by 25%, so,
Let us consider the salary of the officer to be Rs.100.
As the salary of the officer has increased by 25%, therefore the increment in the salary of the officer is
\[\begin{align}
  & 25\%\ of100=\dfrac{25}{100}\times 100 \\
 & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =25 \\
\end{align}\]
Hence, the new salary of the officer is
\[\begin{align}
  & 100+increment=100+25 \\
 & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =125 \\
\end{align}\]
Now, the new salary of the officer should be decreased by Rs.25 to restore the salary of the officer to the original value, therefore the percentage of the salary to be decreased from the new salary is

\[\begin{align}
  & =\left( \dfrac{25}{125}\times 100 \right)\% \\
 & =\left( \dfrac{1}{5}\times 100 \right)\% \\
 & =20\% \\
\end{align}\]
Hence, the percentage of the salary to be decreased from the new salary is 20%.

NOTE:Another way of doing this particular type of question is that we can assume the salary of the officer to be x and then proceed the same procedure as given in the above solution.
The only step at which the student can make an error is where the decreased percentage of the new salary of the officer is to be calculated as it is sometimes confusing what is to be taken in the numerator and what in the denominator. Hence, taking the salary as Rs.100 is advisable.