Question:
The given diagram shows the number of students who failed in an examination comprising papers of English, Hindi and Mathematics. The total number of students who took the test is 500. What is the percentage of students who failed in at least two subjects?
The given diagram shows the number of students who failed in an examination comprising papers of English, Hindi and Mathematics. The total number of students who took the test is 500. What is the percentage of students who failed in at least two subjects?
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When dealing with failure/success in multiple categories, use Venn diagram data carefully, adding only the required intersections.
Updated On: Mar 23, 2026
- 8%
- 8.4%
- 7.8%
- 7.6%
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The Correct Option is C
Solution and Explanation
From the Venn diagram, the number of students who failed in at least two subjects includes:
- Those who failed in exactly two subjects (English and Hindi only, English and Mathematics only, Hindi and Mathematics only)
- Those who failed in all three subjects (English, Hindi, Mathematics)
From the diagram, these numbers are:
- English and Hindi only: 10
- English and Mathematics only: 12
- Hindi and Mathematics only: 12
- All three subjects: 5
Total students who failed in at least two subjects = \(10 + 12 + 12 + 5 = 39\).
Total students who took the test = 500.
Percentage of students who failed in at least two subjects:
\[ \frac{39}{500} \times 100 = 7.8\% \]
Hence, the required percentage is \(\boxed{7.8\%}\).
- Those who failed in exactly two subjects (English and Hindi only, English and Mathematics only, Hindi and Mathematics only)
- Those who failed in all three subjects (English, Hindi, Mathematics)
From the diagram, these numbers are:
- English and Hindi only: 10
- English and Mathematics only: 12
- Hindi and Mathematics only: 12
- All three subjects: 5
Total students who failed in at least two subjects = \(10 + 12 + 12 + 5 = 39\).
Total students who took the test = 500.
Percentage of students who failed in at least two subjects:
\[ \frac{39}{500} \times 100 = 7.8\% \]
Hence, the required percentage is \(\boxed{7.8\%}\).
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