Question

In an examination in which full marks were 500. \[A\] got 25% more than \[C\], \[C\] got 20% less than \[D\]. If \[A\] got 360 marks. What percentage of full marks was obtained by \[D\].
A. 72%
B. 80%
C. 50%
D. 60%

Answer 1

Hint: Here\[A\] got 25% more than \[C\] means, the marks obtained by \[C\] is less than the marks obtained by \[A\]. Similarly, \[C\] got 20% less than \[D\] means, the marks obtained by \[C\] is less than the marks obtained by \[D\]. So, use this concept to reach the solution of the problem.

Complete step-by-step answer:
Given
Total marks of the examination = 500
Marks obtained by \[A\] = 360
Let marks obtained by \[C\]= \[x\]
Since \[A\] got 25% more marks than \[C\], we have
\[
   \Rightarrow x + \dfrac{{25}}{{100}} \times x = 360 \\
   \Rightarrow 100x + 25x = 360 \times 100 \\
   \Rightarrow 125x = 36000 \\
   \Rightarrow x = \dfrac{{36000}}{{125}} \\
  \therefore x = 288 \\
\]
So, marks obtained by \[C\]= 288
Let marks obtained by \[D\]= \[y\]
Since \[C\] got 20% less marks than \[D\], we have
\[
   \Rightarrow y - \dfrac{{20}}{{100}} \times y = 288 \\
   \Rightarrow 100y - 20y = 288 \times 100 \\
   \Rightarrow 80y = 28800 \\
   \Rightarrow y = \dfrac{{28800}}{{80}} \\
  \therefore y = 360 \\
\]
So, marks obtained by \[D\]= 360
The percentage of marks obtained by \[D = \dfrac{{{\text{marks obtained by }}D}}{{{\text{total marks in the examination}}}} \times 100\]
                                                                         \[
   = \dfrac{{360}}{{500}} \times 100 \\
   = 0.72 \times 100 \\
   = 72\% \\
\]
Therefore, the percentage of marks obtained by \[D\] is \[72\% \].
Thus, the correct option is A. 72%.

Note: The marks obtained by \[C\] and \[D\] should not be exceeded by 500 marks because the total marks or maximum marks in the examination is 500. And the percentage of marks should not be exceeded by 100%.