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
- C.4
- D.5
▶ Answer & Explanation
Correct answer: B. 3
Let the maximum marks for each paper be 'M'. The student's marks are proportional to 5, 6, 7, 8, 9, 10. The total marks obtained are the sum of these proportions (5+6+7+8+9+10 = 45 parts). The total maximum marks for 6 papers is 6M. The student scored 60% overall, meaning his total marks are 0.60 * 6M = 3.6M. To find the value of one 'part' in terms of M, we set the total obtained marks (45 parts) equal to 3.6M, so 45 parts = 3.6M, which means 1 part = 3.6M/45 = 0.08M. Now, we need to find how many papers had marks less than 60% of M, which is 0.60M. The marks in the papers are 5 parts, 6 parts, 7 parts, 8 parts, 9 parts, and 10 parts. Converting these to marks: 5 * 0.08M = 0.40M, 6 * 0.08M = 0.48M, 7 * 0.08M = 0.56M, 8 * 0.08M = 0.64M, 9 * 0.08M = 0.72M, 10 * 0.08M = 0.80M. The marks less than 0.60M (60% of max marks) are 0.40M, 0.48M, and 0.56M, which correspond to the first three papers in the proportion.
Source: UPSC csat 2021