Out of 130 students appearing in an examination, 62 failed in English, 52 failed in Mathematics, whereas 24 failed in both English and Mathematics. The number of students who passed finally is
- (a) 40 ✓ UPSC's answer
- (b) 50
- (c) 55
- (d) 60
Why the answer is (a)
• Use the Principle of Inclusion-Exclusion to find the number of students who failed in at least one subject: Failed in English + Failed in Mathematics - Failed in both.
• Calculate the total failures: 62 + 52 - 24 = 90 students.
• Subtract the number of students who failed in at least one subject from the total number of students to find those who passed both: 130 - 90 = 40.
• Therefore, 40 students passed finally, which corresponds to option (a).
Why the other options are wrong
- (b) 50
- Option (b) is incorrect because 50 does not equal the result of 130 - (62 + 52 - 24).
- (c) 55
- Option (c) is incorrect because 55 does not equal the result of 130 - (62 + 52 - 24).
- (d) 60
- Option (d) is incorrect because 60 does not equal the result of 130 - (62 + 52 - 24).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.