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?
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