The following table shows the marks obtained by two students in different subjects : | Subject | Student A | Maximum Marks | Student B | Maximum Marks | | :--- | :---: | :---: | :---: | :---: | | English | 60 | 100 | 80 | 150 | | Psychology | 70 | 100 | 70 | 100 | | History | 50 | 100 | 60 | 100 | | Sanskrit | 30 | 50 | 15 | 25 | The difference in the mean aggregate percentage marks of the students is
- (a) 2·5%
- (b) 13·75%
- (c) 1·25%
- (d) Zero ✓ UPSC's answer
Why the answer is (d)
• Student A's total marks are 60 + 70 + 50 + 30 = 210 out of 100 + 100 + 100 + 50 = 350, so Student A's aggregate percentage is (210/350) × 100 = 60%.
• Student B's total marks are 80 + 70 + 60 + 15 = 225 out of 150 + 100 + 100 + 25 = 375, so Student B's aggregate percentage is (225/375) × 100 = 60%.
• The difference between Student A's aggregate percentage and Student B's aggregate percentage is 60% − 60% = 0%.
• Therefore the official key option (d) Zero follows.
Why the other options are wrong
- (a) 2·5%
- Option (a) 2.5% is wrong because Student A's aggregate percentage is 60% and Student B's aggregate percentage is 60%, so the difference is 0%, not 2.5%.
- (b) 13·75%
- Option (b) 13.75% is wrong because Student A's aggregate percentage is 60% and Student B's aggregate percentage is 60%, so the difference is 0%, not 13.75%.
- (c) 1·25%
- Option (c) 1.25% is wrong because Student A's aggregate percentage is 60% and Student B's aggregate percentage is 60%, so the difference is 0%, not 1.25%.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.