Peter got 30\% of the maximum marks in an examination and failed by 10 marks. However, Paul 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? (M.B.A., 2007)
Answer
Answer (as printed):
Explanation
Let the maximum marks be $x$. Then, $(30\%$ of $x)+10=(40\%$ of $x)-15 \Rightarrow \frac{30}{100}x+10=\frac{40}{100}x-15 \Rightarrow \frac{10x}{100}=25 \Rightarrow x=250$. Passing marks $=(30\%$ of $250)+10=\left(\frac{30}{100}\times 250\right)+10=85$.
Explanation as extracted from the printed page; notation may be imperfect.