28. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

1. A. 15%
2. B. 20%
3. C. 25%
4. D. 35%

Answer: B

Explanation

Let P(E) be the percentage of students who passed in English, and P(H) be the percentage who passed in Hindi. Given: P(E) = 80%, P(H) = 70%. Also, 15% failed in both subjects. This means 100% – 15% = 85% passed in at least one subject. Using the principle of inclusion-exclusion for passing students: P(E U H) = P(E) + P(H) – P(E ∩ H). So, 85% = 80% + 70% – P(E ∩ H). This gives P(E ∩ H) = 150% – 85% = 65% (passed in both). Now, let’s find those who failed in only one subject. Percentage failed in English = 100% – 80% = 20%. Percentage failed in Hindi = 100% – 70% = 30%. Percentage failed in only English = (Failed in English) – (Failed in both) = 20% – 15% = 5%. Percentage failed in only Hindi = (Failed in Hindi) – (Failed in both) = 30% – 15% = 15%. Total percentage failed in only one subject = 5% + 15% = 20%. This question tests set theory concepts applied to percentages.