Question

A gets 30 % marks in an examination but fails by 50 marks, whereas B gets 50 marks more than necessary for passing when he scores 40 %. What is the passing percentage and what are the maximum marks?

• A. 35 %, 1000
• B. 33 %, 1000
• C. 35 %, 900
• D. 33 %, 900

Hint:

Set up equations based on the information given, and solve step by step to find the passing percentage and maximum marks.

Answer 1

The Correct Option is A

Let the maximum marks be \( M \). A's marks are \( 30\% \) of \( M \), and he fails by 50 marks, so the passing marks are: \[ 0.30M + 50 = \text{passing marks} \] B's marks are 40\% of \( M \), and B gets 50 marks more than necessary for passing: \[ 0.40M = \text{passing marks} + 50 \] Equating the two expressions for the passing marks: \[ 0.30M + 50 = 0.40M - 50 \] Solving for \( M \): \[ 100 = 0.10M \quad \Rightarrow M = 1000 \] Thus, the passing percentage is \( \frac{1000 \times 0.35}{100} = 35\% \).