Question

In an examination, A got 10% marks less than B; B got 25% marks more than C and C got 20% less marks than D. If A got 360 marks out of 500, then the percentage of marks obtained by D was-
A. 70
B. 75
C. 80
D. 90

Answer 1

Hint:The concept of percentages and fractions will be required to solve this problem. We have been given the marks obtained by A, so we will use that to find the marks obtained by B, and then C and so on. We will then find the marks obtained by D. We will use them to find the percentage of marks scored by D with respect to 500.

Complete step-by-step answer:
We have been given that A scored 360 marks, which is 10% less than the marks scored by B. Let the marks scored by B be b. So, we can write that-
 $ \begin{align}
  &{\text{b}} - 10\% \;of\;{\text{b}} = 360 \\
  &{\text{b}} - \dfrac{{10}}{{100}} \times {\text{b}} = 360 \\
  &\dfrac{{100{\text{b}} - 10{\text{b}}}}{{100}} = 360 \\
  &\dfrac{{90{\text{b}}}}{{100}} = 360 \\
  &{\text{b}} = 360 \times \dfrac{{100}}{{90}} = 4 \times 100 = 400 \\
\end{align} $

Further, the marks scored by B are 25% more than C. Let the marks obtained by C be c. We can form the equation as-
 $ \begin{align}
  &{\text{c}} + 25\% \;of\;{\text{c}} = {\text{b}} \\
  &{\text{c}} + \dfrac{{25}}{{100}} \times {\text{c}} = 400 \\
  &\dfrac{{100{\text{c}} + 25{\text{c}}}}{{100}} = 400 \\
  &\dfrac{{125{\text{c}}}}{{100}} = 400 \\
  &{\text{c}} = 400 \times \dfrac{{100}}{{125}} = 400 \times \dfrac{4}{5} = 320 \\
\end{align} $
Also, C got 20% marks less than D. The marks obtained by D, d, can be calculated as-
 $ \begin{align}
  &{\text{d}} - 20\% \;of\;{\text{d}} = {\text{c}} \\
  &{\text{d}} - \dfrac{{20}}{{100}} \times {\text{d}} = {\text{c}} \\
  &\dfrac{{100{\text{d}} - 20{\text{d}}}}{{100}} = 320 \\
  &\dfrac{{80{\text{d}}}}{{100}} = 320 \\
  &{\text{d}} = 320 \times \dfrac{{100}}{{80}} = 4 \times 100 = 400 \\
\end{align} $
We need to find the percentage of marks obtained by D, which can be calculated as-
 $ = \dfrac{{\text{d}}}{{Total\;marks}} \times 100 $
 $ = \dfrac{{400}}{{500}} \times 100 = 80\% $
This is the required answer. The correct option is C.

Note: A common mistake here is that students forget to find the percentage of the marks obtained by D, and instead just find the total marks obtained by D. Also, we often write the equation 360 + 10% of 360 = b instead of b - 10% of b = 360, which is incorrect. More importantly while calculating the marks of say “c” we must consider the percentage of marks of that of B obtained from A not directly from A.