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%

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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.

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%.