A candidate scores 45% of the total marks in an examination but still falls short of the pass mark by 40 marks. If the pass percentage is 55%, what are the maximum possible marks in the exam?

Introduction / Context:

This question tests the core percentage concept of relating a candidate's obtained marks, pass percentage, and maximum marks in an examination. It is a very common aptitude pattern where the difference between two percentages of the same total is given as an absolute number of marks. Learning to convert such information into a simple linear equation helps in quickly finding the maximum marks and is very useful for competitive exams.

Given Data / Assumptions:

• The candidate scores 45% of the total marks.
• The pass percentage for the exam is 55% of the total marks.
• The candidate fails by 40 marks, which means the pass marks are 40 more than the candidate's marks.
• We assume a single exam with a fixed maximum mark M.

Concept / Approach:

The key idea is that both the candidate's marks and the pass marks are percentages of the same maximum marks M. The difference between 55% and 45% is 10% of M. This 10% of M is numerically equal to 40 marks. Once we know that 10% corresponds to 40, we can scale up to find 100% of the total marks.

Step-by-Step Solution:

Verification / Alternative check:

If the maximum marks are 400, then 45% of 400 is 0.45 * 400 = 180 marks. The pass marks are 55% of 400, which is 0.55 * 400 = 220 marks. The difference between 220 and 180 is 40 marks, which exactly matches the statement that the candidate fails by 40 marks. This confirms that 400 is correct.

Why Other Options Are Wrong:

• 300: Ten percent of 300 is 30, so the difference between 45% and 55% would be 30 marks, not 40.
• 350: Ten percent of 350 is 35, so the shortfall would be 35 marks, which does not match the given 40 marks.
• 450: Ten percent of 450 is 45, so the shortfall would become 45 marks, not 40.
• 550: Ten percent of 550 is 55, again inconsistent with the given difference of 40 marks.

Common Pitfalls:

Students sometimes directly take 10% of the candidate's marks instead of 10% of the total marks, which is incorrect. Another common mistake is to subtract 45 from 55 and treat 10 as marks instead of a percentage. It is also easy to mix up pass percentage with pass marks. Always remember that both percentages act on the same unknown total M, so the difference in percentages multiplied by M gives the mark difference.

Final Answer:

The maximum possible marks in the exam are 400.