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In an examination 70% candidates passed in prelims and 55% candidates passed in Mains. If 62% candidates passed in both these subjects, then what per cent of candidates failed in both the exams?
  • a)
    37%
  • b)
    26%
  • c)
    43%
  • d)
    15%
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In an examination 70% candidates passed in prelims and 55% candidates ...
Students passed in Prelims = 70%
Students passed in Mains = 55%
Students passed in both  = 62%
No of students passed in at least one subject = (70+55)-62 = 63%.
students failed in both subjects = 100-63 = 37%.
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Most Upvoted Answer
In an examination 70% candidates passed in prelims and 55% candidates ...
Understanding the Problem
To determine the percentage of candidates who failed in both the prelims and Mains exams, we will use the principle of inclusion-exclusion.
Data Given
- Percentage of candidates who passed prelims: 70%
- Percentage of candidates who passed Mains: 55%
- Percentage of candidates who passed both exams: 62%
Calculating Candidates Passing at Least One Exam
Using the inclusion-exclusion principle, we can find the percentage of candidates who passed at least one exam:
- Percentage who passed at least one exam = (Percentage passed prelims) + (Percentage passed Mains) - (Percentage passed both)
- This translates to:
70% + 55% - 62% = 63%
Finding Candidates Who Failed Both Exams
To find the percentage of candidates who failed both exams, we subtract the percentage of those who passed at least one exam from 100%:
- Percentage who failed both = 100% - Percentage who passed at least one exam
- This gives us:
100% - 63% = 37%
Conclusion
Thus, the percentage of candidates who failed in both prelims and Mains exams is 37%. Therefore, the correct answer is option 'A'.
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In an examination 70% candidates passed in prelims and 55% candidates passed in Mains. If 62% candidates passed in both these subjects, then what per cent of candidates failed in both the exams?a)37%b)26%c)43%d)15%Correct answer is option 'A'. Can you explain this answer?
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