# 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

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328.2k+ views

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%.

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%.

Last updated date: 01st Jun 2023

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