A) 800
B) 900
C) 1,000
D) 1,100
Correct Answer: A
Solution :
Let the full marks = x First candidates gets 30% of x in exam i.e., he gets \[\frac{a}{b}=\left( \frac{a}{b}\times 100 \right)%\] marks m the exam Now, another candidate gets 320 marks and fails by 30 marks. \[\text{Percentage increase=}\left( \frac{\text{Increase in quantity}}{\text{Original quantity}}\text{ }\!\!\times\!\!\text{ 100} \right)\text{ }\!\!%\!\!\text{ }\] Passing marks \[\text{Percentage decrease =}\left( \frac{\text{Decrease in quantity}}{\text{Original quantity}}\text{ }\!\!\times\!\!\text{ 100} \right)\text{ }\!\!%\!\!\text{ }\] Now, first candidate fails by 50 marks \[\left\{ \frac{x}{(100+x)}\times 100 \right\}%\] Passing marks for him \[\left\{ \frac{x}{(100-x)}\times 100 \right\}%\] But he gets \[=\left\{ \left( \frac{r}{r+100} \right)\times 100 \right\}%\] marks \[=\left\{ \left( \frac{r}{r-100} \right)\times 100 \right\}%\] \[S.P.-C.P\] \[S.P.\text{ }>\text{ }C.P.\] \[C.P.-S.P\] \[C.P.\text{ }>\text{ }S.P.\] Maximum marks = 800.
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