Question

A student scores 25% of the total marks of a paper and fails by 30 marks. Another student scores 35% of total marks and fails by 5 marks. What is the pass mark for that paper?

• A. 85
• B. 82.5
• C. 92.5
• D. 90
• E. None of these

Answer 1

The Correct Option is C

Step 1: Understand the given information.
- The first student scores 25% of the total marks and fails by 30 marks.
- The second student scores 35% of the total marks and fails by 5 marks.
We need to find the pass mark for the paper.

Step 2: Define the total marks.
Let the total marks of the paper be \( x \).
- The first student scores \( 25\% \) of \( x \), i.e., \( \frac{25}{100} \times x = 0.25x \).
- The second student scores \( 35\% \) of \( x \), i.e., \( \frac{35}{100} \times x = 0.35x \).

Step 3: Set up equations based on the given conditions.
- The first student fails by 30 marks, so the pass mark is \( 0.25x + 30 \).
- The second student fails by 5 marks, so the pass mark is \( 0.35x + 5 \).
Since both students are failing at the same pass mark, we can set up the following equation:
\( 0.25x + 30 = 0.35x + 5 \)

Step 4: Solve for \( x \).
Simplifying the equation:
\( 0.25x + 30 = 0.35x + 5 \)
\( 30 - 5 = 0.35x - 0.25x \)
\( 25 = 0.10x \)
\( x = \frac{25}{0.10} = 250 \)

Step 5: Calculate the pass mark.
Now that we know the total marks \( x = 250 \), we can calculate the pass mark using either of the equations:
Pass mark = \( 0.25 \times 250 + 30 = 62.5 + 30 = 92.5 \)

Step 6: Conclusion.
The pass mark for the paper is 92.5.

Final Answer:
The correct option is (C): 92.5.