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 ?
- (a) 2
- (b) 3 ✓ UPSC's answer
- (c) 4
- (d) 5
Why the answer is (b)
• Let the marks be 5k, 6k, 7k, 8k, 9k and 10k, a total of 45k, and let the maximum in each paper be M.
• Overall 60% means 45k = 0·6 × 6M = 3·6M, so M = 12·5k and 60% of M = 7·5k.
• Papers with less than 7·5k: 5k, 6k and 7k — three papers.
• Hence option (b).
Why the other options are wrong
- (a) 2
- Three papers (5k, 6k, 7k) are below 7·5k, not two.
- (c) 4
- Only three papers are below 7·5k; 8k is above 60% of the maximum.
- (d) 5
- Only three papers are below 7·5k; 8k and 9k are above 60% of the maximum.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.