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:

Translate word problem to equations. Use one variable and set both passing mark expressions equal to solve.

Answer 1

The Correct Option is A

Let the maximum marks be \( M \) Step 1: A’s marks and passing condition \[ \text{A’s marks} = 0.30M
\Rightarrow \text{Passing marks} = 0.30M + 50 \] Step 2: B’s marks and passing condition \[ \text{B’s marks} = 0.40M
\Rightarrow \text{Passing marks} = 0.40M - 50 \] Step 3: Equating both expressions for passing marks \[ 0.30M + 50 = 0.40M - 50
\Rightarrow 100 = 0.10M \Rightarrow M = \boxed{1000} \] Step 4: Passing percentage \[ \text{Passing marks} = 0.30 \times 1000 + 50 = 300 + 50 = 350
\text{Passing %} = \frac{350}{1000} \times 100 = \boxed{35%} \]