Question

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

• A. 85
• B. 90
• C. 95
• D. 100

Answer 1

The Correct Option is B

Let the maximum marks be denoted by \( M \). Aman scored 30% of \( M \) and failed by 15% of \( M \). Therefore, the passing marks are \( 30\% \, M + 15\% \, M = 45\% \, M \). Mathematically, this is: \( 0.30M + 0.15M = 0.45M \). Anil scored 40% of \( M \) and was 10 marks above the passing marks, hence \( 40\% \, M = 45\% \, M + 10 \). Expressing this mathematically: \[ 0.40M = 0.45M - 10 \] Simplify and solve for \( M \): \[ 0.40M + 10 = 0.45M \] \[ 10 = 0.45M - 0.40M \] \[ 10 = 0.05M \] Divide both sides by 0.05 to find \( M \): \[ M = \frac{10}{0.05} \] \[ M = 200 \] Now, calculate the passing marks which are 45% of \( M \): \[ \text{Passing Marks} = 0.45 \times 200 = 90 \] Therefore, the passing marks are 90.