In an examination, a student needs to secure 24% of the maximum marks to pass.\nThe student scores 61 marks and fails by 29 marks.\nWhat are the maximum marks for this examination?

Introduction / Context:
This question focuses on passing marks expressed as a percentage of the maximum marks and uses information about how many marks a student falls short by. Such problems are frequent in aptitude exams and help reinforce the relationship between percentages, absolute marks, and required thresholds.

Given Data / Assumptions:

• A student must secure 24% of the maximum marks to pass.
• The student actually scores 61 marks.
• The student fails by 29 marks, which means the student scored that many marks fewer than the passing mark.
• We need to find the maximum marks for the exam.

Concept / Approach:
The key observation is that failing by 29 marks means the passing mark is 61 + 29. This passing mark represents 24% of the maximum marks. Once we compute the passing mark, we set up an equation passing mark = 24% of total marks and solve for the total. This is a direct reverse percentage problem in the context of examination scores.

Step-by-Step Solution:
Step 1: Let the maximum marks be M.Step 2: The passing marks are 24% of M, so passing marks = 24 / 100 * M = 0.24 * M.Step 3: The student scores 61 marks and fails by 29 marks, so passing marks = 61 + 29 = 90 marks.Step 4: Set up the equation 0.24 * M = 90.Step 5: Solve for M: M = 90 / 0.24 = 375.

Verification / Alternative check:
To verify, calculate 24% of 375. We get 375 * 24 / 100 = 375 * 0.24 = 90 marks. If the passing mark is 90 and the student scored 61, then the shortfall is 90 - 61 = 29 marks, exactly as described in the problem. Therefore, the computed maximum marks of 375 are consistent with all details given in the question.

Why Other Options Are Wrong:
If the maximum marks were 400, then 24% of 400 would be 96, giving a shortfall of 96 - 61 = 35, not 29.
If the maximum marks were 425, then 24% of 425 would be 102, leading to a different shortfall.
If the maximum marks were 450, then 24% of 450 would be 108, which does not match the required failing margin.
300 marks would give a passing mark of 72, and the student would fail by only 11 marks, which is again inconsistent.

Common Pitfalls:
Students sometimes misinterpret "fails by 29 marks" and treat 29 as 24% of the maximum marks, which is incorrect. Another common mistake is to forget to add the shortfall to the obtained marks to compute the passing marks. Always convert verbal descriptions about failure or success into clear equations linking obtained marks, passing marks, and percentages. Writing these relationships step by step avoids confusion and leads to accurate results.

Final Answer:
The maximum marks for the examination are 375 marks.