[85] Arun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took

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Arun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?

250

Explanation:

Let maximum marks of the examination $=x$

Marks that Arun got $=30%$ of $x$ $=\dfrac{30x}{100}$

Given that Arun failed by 10 marks.

=> pass mark = $\dfrac{30x}{100}+10~~\cdots(1)$

Marks that Sujith got $=40%$ of $x$ $=\dfrac{40x}{100}$

Given that Sujith got 15 marks more than the passing marks.

=> pass mark $=\dfrac{40x}{100}-15~~\cdots(2)$

From $(1)$ and $(2)$,

$\dfrac{30x}{100}+10=\dfrac{40x}{100}-15\dfrac{10x}{100}=25\dfrac{x}{10}=25x=10×25=250$

pass mark

$=\dfrac{30x}{100}+10$

$\dfrac{30×250}{100}+10$

=75+10=85

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