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
- B.50
- C.55
- D.60
▶ Answer & Explanation
Correct answer: B. 50
To find the number of students who passed, we first determine the number who failed in at least one subject. Using the principle of inclusion-exclusion for sets, the number failing in English or Mathematics is (Failed in English) + (Failed in Mathematics) - (Failed in Both). This gives 62 + 52 - 24 = 90 students who failed in at least one subject. The total number of students is 130. Therefore, the number of students who passed in both subjects is the total number of students minus those who failed in at least one subject: 130 - 90 = 40. There seems to be a discrepancy with the provided correct answer 'B' (50). Re-evaluating the calculation: Students failing only in English = 62 - 24 = 38. Students failing only in Maths = 52 - 24 = 28. Total failing in at least one subject = (Failing only in English) + (Failing only in Maths) + (Failing in Both) = 38 + 28 + 24 = 90. Number of students who passed = Total Students - Total failing = 130 - 90 = 40. There is a consistent result of 40 students passing. The provided answer B (50) is incorrect based on standard set theory calculations for this problem. Assuming the question implies passing *both* subjects, the calculation is as follows: Total students = 130. Failed in English = 62. Failed in Mathematics = 52. Failed in Both = 24. Failed in English ONLY = 62 - 24 = 38. Failed in Mathematics ONLY = 52 - 24 = 28. Total students failed in AT LEAST ONE subject = (Failed English ONLY) + (Failed Maths ONLY) + (Failed Both) = 38 + 28 + 24 = 90. Students who PASSED (i.e., passed both English and Mathematics) = Total Students - Total Students Failed in AT LEAST ONE subject = 130 - 90 = 40. The provided correct answer 'B' (50) is mathematically inconsistent with the problem statement.
Source: UPSC csat 2015