Question

In an examination, a student requires $40\%$ of the total marks to pass. Ritu gets 185 marks and fails by 15 marks. Find the total marks.

Answer 1

Hint: We need to assume the total marks of the examination and take a variable. Then we need to find the passing marks with respect to the total marks. We also have the information that Ritu gets 185 marks and fails by 15 marks. We use that to find the linear equation of the variable. We solve it to find the solution of the problem.

Complete step by step answer:
Let’s assume that the total marks of the examination are x.
Ritu requires 40% of the total marks to pass.
So, the marks that Ritu needs is $40\%$ of x which is $\dfrac{40x}{100}$.
Now Ritu got 185 marks and failed by 15 marks.
So, Ritu would have passed if she got 15 marks more.
The addition of 15 to the number 185 would be equal to the number $\dfrac{40x}{100}$.
We get the linear equation by expressing the conditions as $\dfrac{40x}{100}=185+15$.
Now we solve the equation by applying the binary operations.
$\begin{align}
  & \dfrac{40x}{100}=185+15=200 \\
 & \Rightarrow x=\dfrac{200\times 100}{40}=5\times 100=500 \\
\end{align}$

The total marks of the examination were 500.

Note: We can solve the problem taking the difference of the passing marks and the marks that she got as 15. Although the equation will be the same, the formation of the linear equation will be different. We can also solve it by taking the total marks on the basis of hundreds. For example, we take the total marks as 100 to find the passing marks with respect to the total marks. We use that to find the linear equation. We solve it to find the solution of the problem.