A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5: 6: 7: 8: 9: 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?
Answer & explanation
Answer: (b) 3
With equal maximum marks, the overall 60% equals the average of the six papers' shares, and the average of 5 to 10 is 7.5. Only the papers with shares 5, 6 and 7 fall below that level — 3 papers.
- Let the marks be 5k, 6k, 7k, 8k, 9k and 10k; the total is 45k.
- Since every paper has the same maximum, the overall 60% equals the average paper score: 45k ÷ 6 = 7.5k is 60% of the maximum.
- Papers below 7.5k: 5k, 6k and 7k — 3 papers.
- Check: if the maximum is 12.5k, the marks are 40%, 48%, 56%, 64%, 72%, 80% — three below 60%.
Remember · When maximum marks are equal, the overall percentage is the average of the paper percentages; compare each paper with the mean.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·