Pass in both subjects – complement of union of failures: In an examination, 30% of students failed in Hindi, 45% failed in English, and 20% failed in both. What percentage passed in both subjects?

Introduction / Context:
Passing both subjects is the complement of failing at least one subject. The failure sets overlap; use inclusion-exclusion, then subtract from 100%.

Given Data / Assumptions:

• % fail Hindi = 30%
• % fail English = 45%
• % fail both = 20%

Concept / Approach:
|Fail H ∪ Fail E| = 30 + 45 − 20 = 55. Therefore, % passing both = 100 − 55.

Step-by-Step Solution:
Fail at least one = 55%Pass both = 100% − 55% = 45%

Verification / Alternative check:
Venn logic confirms the complement relationship between passing both and failing at least one.

Why Other Options Are Wrong:
35%, 35.7%, 40% do not match the inclusion-exclusion result.

Common Pitfalls:
Adding 30 and 45 without subtracting the overlap 20.

Final Answer:
45%