Question

Passing percentage marks in an exam are 40%. A student obtained 72 marks out of 200. By what percent did he fail?
A. 8
B. 5
C. 4
D. 3

Answer 1

Hint: The formula for finding x percentage of any quantity 1 is
\[\dfrac{x}{100}\times Quantity\ 1\]
Another important formula for percentage questions is
\[\dfrac{Quantity\ 1}{Quantity\ 2}\times 100\]

Complete Step-by-step answer:
As mentioned in the question, the passing percentage in an exam is 40%,
The total or the maximum marks of the exam is given in the question as 200 marks.
Hence, the passing marks in the exam is given as follows
\[\begin{align}
  & 40\%\ of200 \\
 & =\dfrac{40}{100}\times 200 \\
 & =80 \\
\end{align}\]
So, the passing marks in the exam are 80 marks.
As a student he got 72 out of 200 marks, so he failed the exam by 8 marks.
Now, 72 out of 200 in terms of percentage is
\[\begin{align}
  & =\dfrac{72}{200}\times 100 \\
 & =36\% \\
\end{align}\]
Hence, the percent by which he failed is given as follows
\[\begin{align}
  & =(40-36)\% \\
 & =4\% \\
\end{align}\]
Therefore, the student failed the exam by 4%.

Note: It would be difficult for a student to figure out the solution if he or she does not know this fact which is mentioned as follows
The formula for finding x percentage of any quantity 1 is
\[\dfrac{x}{100}\times Quantity\ 1\]
Now, the students can make an error if they don’t know that percentages are to be subtracted for finding ‘by how much did the student fail ‘as it might look tricky.
The students can make an error while solving this question if this above formula is unknown to the students.