In an examination, 35% is the minimum percentage required to pass. A student scores 200 marks but still fails by 24 marks. What are the maximum total marks of the examination?

Introduction / Context:
This question checks understanding of passing percentage and maximum marks. It is a common type of aptitude problem where the candidate must relate the marks obtained, the margin by which the student fails, and the required passing percentage to compute the total marks of the exam.

Given Data / Assumptions:

• Passing percentage = 35 percent.
• Marks obtained by the student = 200.
• The student fails by 24 marks.
• Maximum marks of the examination = unknown (let it be M).
• Passing marks are calculated as 35 percent of M.

Concept / Approach:
The key idea is that failing by 24 marks means the pass mark is 24 marks more than the marks obtained. So: Passing marks = 200 + 24 = 224. At the same time, passing marks are 35 percent of maximum marks. Therefore: 0.35 * M = 224. We can solve this equation to find M, the maximum marks.

Step-by-Step Solution:
Step 1: Interpret "fails by 24 marks". It means passing marks = obtained marks + 24. Step 2: So passing marks = 200 + 24 = 224. Step 3: Passing marks are 35 percent of total marks, so 35/100 * M = 224. Step 4: Write this as 0.35 * M = 224. Step 5: Solve for M: M = 224 / 0.35. Step 6: Divide to get M = 640.

Verification / Alternative check:
Check with M = 640. Passing marks = 35 percent of 640 = 0.35 * 640 = 224. The student has 200 marks, so shortfall = 224 - 200 = 24 marks, which matches the given failure margin. Thus the calculated maximum marks are consistent with the question statement.

Why Other Options Are Wrong:
550: 35 percent of 550 is 192.5, which does not differ from 200 by 24 marks. 680: 35 percent of 680 is 238, which again does not match the failing margin of 24 marks. 820: 35 percent of 820 is 287, which is far from the required pass mark. 600: 35 percent of 600 is 210, and the difference from 200 is 10, not 24.

Common Pitfalls:
Many students confuse "fails by 24 marks" with "scores 24 percent less than passing marks", which is incorrect. The phrase refers to a simple difference in raw marks. Another common error is to treat 35 percent of 200 as the pass mark, rather than 35 percent of the unknown total. Always express passing marks in terms of the total maximum marks, set up an equation, and then solve for the unknown quantity.

Final Answer:
The maximum marks of the examination are 640.