Question

Shilpa got a 20% increase in her salary. If her new salary is Rs. 1,75,000, find her original salary.

Answer 1

Hint: Here, we have been told that Shilpa got a 20% increase in her salary and her salary now is Rs. 175000 and we have to find her original salary. For this, we will first assume the original salary of Shilpa to be ‘x’. Thus, we have to find the value of x. Then we will find the increase in her salary in terms of x as it will be equal to 20% of x. Then we will write her new salary in terms of x as the sum of her original salary and the increase in it and then we will keep it equal to the given new salary of her. Thus, we will get an equation in x, solving that equation, we will get the required answer.

Complete step-by-step solution:
Here, we have been told that Shilpa got a 20% increase in her salary and her salary now is Rs. 175000 and we have to find her original salary. For this, let us first assume her original salary to be ‘x’.
Since the increase on her salary is of 20%, we can write the increase on Shilpa’s salary as 20% of x, which is given as:
$\begin{align}
  & \dfrac{20}{100}\times x \\
 & \Rightarrow \dfrac{1}{5}\times x \\
 & \Rightarrow \dfrac{x}{5} \\
\end{align}$
Now, the new salary of Shilpa will be equal to the sum of her original salary and the increase in her salary.
Thus, the new salary of Shilpa is given as:
$x+\dfrac{x}{5}$
Now, we have also been given that the new salary of Shilpa is equal to Rs. 175000.
Thus, we can say that:
$x+\dfrac{x}{5}=175000$
Now, solving this equation, we will get:
$\begin{align}
  & \dfrac{6x}{5}=175000 \\
 & \Rightarrow x=175000\times \dfrac{5}{6} \\
 & \therefore x=145833.33 \\
\end{align}$
Thus, the original salary of Shilpa was Rs. 145833.33.

Note: We could have also written the new salary directly equal to $\dfrac{6x}{5}$ as follows:
The raise on the salary of Shilpa was 20%. Thus, her new salary is equal to 120% of her old salary. Thus, we can say that:
$\begin{align}
  & \dfrac{120}{100}\times x=175000 \\
 & \Rightarrow \dfrac{6x}{5}=175000 \\
 & \therefore x=14583.33 \\
\end{align}$