Passing threshold and shortfall: A student must score 780 marks to pass. Sonu scored 728 and failed by 5%. What are the maximum aggregate marks?

Introduction / Context:
This question connects a fixed pass mark with a stated failure margin in percentage terms of the aggregate (total) marks. The key is to interpret “failed by 5%” as a shortfall equal to 5% of the total possible marks.

Given Data / Assumptions:

• Pass mark = 780.
• Sonu’s mark = 728.
• Shortfall to pass = 780 − 728 = 52.
• “Failed by 5%” ⇒ Shortfall = 5% of total aggregate.

Concept / Approach:
Let total marks be M. Then 5% of M equals the shortfall 52. Solve M from 0.05M = 52. This yields the required aggregate marks for the exam.

Step-by-Step Solution:
Shortfall = 780 − 728 = 52Interpretation: 52 = 5% of total ⇒ 52 = 0.05 * MM = 52 / 0.05 = 1040

Verification / Alternative check:
5% of 1040 is 52. Adding this to Sonu’s 728 gives 780, the pass mark. Thus the interpretation and arithmetic are consistent.

Why Other Options Are Wrong:
1000 gives 5% = 50 (short by 2); 1100 gives 55 (too large); “Cannot be determined” is incorrect since the shortfall percentage is specified.

Common Pitfalls:
Misreading “failed by 5%” as 5% of 780 or 5% of Sonu’s marks; the standard usage is relative to the total possible marks.

Final Answer:
1040