Question

Rahul got 150 marks in a test, he scored 25% more marks than the pass marks in it. Rajesh got 165 marks in it. By what percent did his marks exceed the pass marks?

Answer 1

Hint: Assume that the pass mark is $x$. Then form a linear equation in one variable according to the given conditions. Find out 25% of $x$ and add it to the pass marks. Equate the obtained sum with 150 and find the value of $x$. Once pass marks are obtained, subtract it from the marks of Rajesh and find the percentage of the exceeded marks.

Complete step-by-step answer:
Let us assume that the pass marks are $x$. According to the given conditions, Rahul obtained 25% more marks than the pass marks. Therefore mathematically,
\[\begin{align}
  & x+25\%\text{ of }x=150 \\
 & \Rightarrow x+\dfrac{x}{4}=150 \\
 & \Rightarrow \dfrac{5x}{4}=150 \\
 & \Rightarrow x=120 \\
\end{align}\]
Therefore, the pass marks are 120.
Now, it is known that Rajesh got 165 marks. Therefore, Rajesh obtained $165-120=45$ marks more than the pass marks. So, percentage of marks Rajesh exceeded than the pass marks
$\begin{align}
  & =\dfrac{45}{120}\times 100\% \\
 & =\dfrac{150}{4}\% \\
 & =37.5\% \\
\end{align}$
Hence, Rajesh exceeded the pass marks by 37.5%.

Note: Do not get confused in the words of the question. We have added $\left( \dfrac{1}{4} \right)$ of the pass marks to the pass marks because it is given that Rahul obtained 25% more than the pass marks. Now, when we are finding the percentage of marks Rajesh exceeded, we have divided the difference of Rajesh marks and pass marks with the pass marks. This is because we are finding the percentage exceeded from pass marks.