Percent passed in Hindi given failure rates and overlap: In an exam, 40% students failed in Hindi, 50% failed in English, and 21% failed in both. What percentage passed in Hindi?

Introduction / Context:
When a problem asks for the percentage that passed a subject, you subtract the subject’s fail percentage from 100%. The overlap with another subject is irrelevant unless asked about combined categories like “failed at least one.”

Given Data / Assumptions:

• Failed Hindi = 40%
• Failed English = 50%
• Failed both = 21%

Concept / Approach:
“Passed in Hindi” means did not fail Hindi. Therefore % passed in Hindi = 100% − % failed in Hindi = 60%. No further inclusion–exclusion is needed for this specific query.

Step-by-Step Solution:
Passed Hindi = 100 − 40 = 60%

Verification / Alternative check:
If needed, a Venn picture shows that all categories together sum to 100%; the complement of “failed Hindi” is “passed Hindi.”

Why Other Options Are Wrong:
31%, 55% are unrelated; 40% is the fail rate; 60% uniquely matches the complement.

Common Pitfalls:
Overcomplicating with intersections when the question is a single-subject complement problem.

Final Answer:
60%