Question

A medical student has to score $40\%$ marks to pass. He gets 80 marks and fails by 60 marks. Find the maximum number of marks.

Answer 1

Hint: Assume the maximum number of marks equal to $x$. Find the value of $40\%$ of $x$ and equate it with the sum of marks obtained by the student and the number of marks by which he failed. Form a linear equation in one variable $x$ and solve for its value to get the maximum number of marks.

Complete step by step answer:
Here, let us assume the maximum number of marks equal to $x$. It is given that the medical student has to secure $40\%$ marks to pass. Therefore, mathematically,
Marks obtained to pass = $40\%$ of $x$
$\Rightarrow $ Passing marks = $\dfrac{40}{100}\times x$
$\Rightarrow $ Passing marks = $\dfrac{4x}{10}\ldots \ldots \ldots \left( i \right)$
Now, we have been provided that the student obtained 80 marks and fails by 60 marks. So, we can say that the total passing marks is the sum of marks obtained by the student and the number of marks by which he failed. Therefore, we have,
$\Rightarrow $ Passing marks = $80+60=140\ldots \ldots \ldots \left( ii \right)$
From equation (i) and (ii), we get,
$\dfrac{4x}{10}=140$
By cross multiplication, we get,
$\begin{align}
  & \Rightarrow x=\dfrac{1400}{4} \\
 & \Rightarrow x=350 \\
\end{align}$

Hence, the maximum number of marks is 350.

Note: One may note that we have to calculate $40\%$ of total marks, that is, $x$ to get the total marks required to pass. We must not calculate $40\%$ of 140 otherwise we will get the wrong expression and answer. To solve the above question, we must know how to calculate percentage. You may see that we have equated the two expressions of passing marks to form a linear equation. This is because we were provided with the information regarding passing marks only.