Question

A candidate scored 25% and failed by 30 marks and another candidate scored 50% and got 20 marks more than the minimum marks required to pass. Find the maximum marks and the passing marks.

Answer 1

Hint: For solving this question you should know about the percentage concept. In this problem, first we will assume the maximum marks and then we will make an equation for minimum passing marks and then set the equation according to the given details in the question. And thus we get the maximum marks and then calculate the minimum passing marks by the relation which is provided in the question.

Complete step by step answer:
According to the question it is asked to find the maximum marks and the passing marks and the given details are, A candidate scored 25% and failed by 30 marks and another candidate scored 50% and passed by 20 marks more than the passing marks.
So, let the maximum marks be $x$.
And the minimum marks to pass \[=25\% \text{ of }x+30\]
We can write it as: $\dfrac{x}{4}+30$
Now according to the question,
$\begin{align}
  & \Rightarrow \dfrac{x}{4}+30=\dfrac{x}{2}-20 \\
 & \Rightarrow \dfrac{x}{2}-\dfrac{x}{4}=30+20 \\
 & \Rightarrow x=50\times 4=200 \\
\end{align}$
Hence the maximum marks to be obtained are 200.
Now the minimum passing marks $=\dfrac{200}{4}+30=80$.
Hence the maximum marks are 200 and the minimum passing marks are 80.

Note: While solving this type of questions there are always some conditions given to us for making information for the equation. So, we use that condition or information and then we will solve the equations and get the required answer for the question.