In an examination, a student must score 25% of the total marks to pass. He scores 47 marks and fails by 43 marks. What are the maximum marks of the examination?

Introduction / Context:
This question is very similar to other passing-percentage problems and reinforces the technique of relating marks obtained, marks needed to pass, and the percentage requirement to find the total marks of the exam.

Given Data / Assumptions:

• Passing percentage = 25 percent.
• Marks obtained by the student = 47.
• The student fails by 43 marks.
• Maximum marks of the examination = unknown (let it be M).
• Passing marks are 25 percent of M.

Concept / Approach:
As before, failing by 43 marks means: Passing marks = Marks obtained + Shortfall = 47 + 43. These passing marks must equal 25 percent of the total marks: Passing marks = 25/100 * M = 0.25 * M. We set up the equation 0.25 * M = 47 + 43 and solve for M.

Step-by-Step Solution:
Step 1: Shortfall in marks = 43. Step 2: Passing marks = 47 + 43 = 90. Step 3: Passing marks are 25 percent of M, so 0.25 * M = 90. Step 4: Solve for M: M = 90 / 0.25. Step 5: Compute 90 / 0.25 = 360. Step 6: Therefore, maximum marks M = 360 marks.

Verification / Alternative check:
Check the result using M = 360. Passing marks at 25 percent = 0.25 * 360 = 90. The student has 47 marks, and the shortfall is 90 - 47 = 43 marks, which exactly matches the given information. So the computed total marks are correct.

Why Other Options Are Wrong:
385 marks: 25 percent of 385 is 96.25, giving a different shortfall. 410 marks: 25 percent of 410 is 102.5, not matching the provided data. 435 marks: 25 percent of 435 is 108.75, again inconsistent. 320 marks: 25 percent of 320 is 80, and the difference from 47 is 33, not 43.

Common Pitfalls:
Students sometimes mistake the shortfall as a percentage rather than a fixed number of marks. Others may apply the 25 percent to the marks obtained instead of the total marks. The safe method is always to express passing marks in two ways: as a numerical sum (obtained plus shortfall) and as the required percentage of the total, then solve for the total.

Final Answer:
The maximum marks of the examination are 360 marks.