Question

Aditya’s salary is $80\%$ of Amit’s salary and $120\%$ of Rajiv’s salary. What is Amit’s salary if Rajiv’s salary is $30000$?
A. $40000$
B. $45000$
C. $50000$
D. $55000$

Answer 1

Hint: First let us assume Aditya’s salary be $x$ and Amit’s salary be $y$. Then, by using information given in the question that Aditya’s salary is $80\%$ of Amit’s salary and $120\%$ of Rajiv’s salary, we form two equations. When we solve these equations, we get our answer.

Complete step-by-step solution:
We have given that Rajiv’s salary is $30000$. Aditya’s salary is $80\%$ of Amit’s salary and $120\%$ of Rajiv’s salary.
Let us assume Aditya’s salary be $x$ and Amit’s salary be $y$.
We have to find the Amit’s salary.
As given Aditya’s salary is $120\%$ of Rajiv’s salary.
So, Aditya’s salary will be $x=120\%\text{ of }30000$
When we solve further, we get
$\begin{align}
  & x=\dfrac{120}{100}\times 30000 \\
 & x=36000 \\
\end{align}$
Now, we have given that Aditya’s salary is $80\%$ of Amit’s salary.
So, we get the equation,
$x=80\%\text{ of y}$
When we put the value of $x$ in above equation, we get
$\begin{align}
  & 36000=\dfrac{80}{100}\times y \\
 & 36000=\dfrac{4}{5}\times y \\
\end{align}$
To get the value of $y$, we cross multiply the equation,
$\begin{align}
  & y=\dfrac{36000\times 5}{4} \\
 & y=45000 \\
\end{align}$
So, Amit’s salary is $45000$.
Option B is the correct answer.

Note: As there are two unknown quantities in the question, so we have to assume two variables. As there are two unknown variables, we have two equations. The confusing line given in the question is Aditya’s salary is $80\%$ of Amit’s salary and $120\%$ of Rajiv’s salary. Some students may consider Amit’s salary is $120\%$ of Rajiv’s salary. So, be careful and read twice the question and then go ahead.