In an examination, 35 percent of the students failed in Hindi, 45 percent failed in English and 20 percent failed in both subjects. What percentage of students passed in both Hindi and English?

Introduction / Context:
This problem tests knowledge of set theory and percentage, specifically the use of the inclusion exclusion principle for two sets. The sets here represent failures in Hindi and English, and we are required to determine the percentage that passes in both subjects.

Given Data / Assumptions:

• 35 percent students fail in Hindi.
• 45 percent students fail in English.
• 20 percent students fail in both Hindi and English.
• Every student either passes or fails in each subject.

Concept / Approach:
Let H be the set of students who fail in Hindi and E be the set of students who fail in English. We know percentages of H, E and H intersection E. Using the formula for union of two sets, we can find the percentage that fail in at least one subject. The complement of that union gives the percentage that pass in both subjects.

Step-by-Step Solution:
Percentage failing in Hindi = 35 percent.Percentage failing in English = 45 percent.Percentage failing in both = 20 percent.Percentage failing in at least one subject = 35 + 45 - 20 = 60 percent.Therefore, percentage passing in both subjects = 100 - 60 = 40 percent.

Verification / Alternative check:
Assume there are 100 students. Then 35 fail Hindi, 45 fail English and 20 fail both. Using a Venn diagram or simple counting, at least one failure occurs in 60 students, leaving 40 students who do not belong to either failure set. Hence they pass both subjects, confirming the answer of 40 percent.

Why Other Options Are Wrong:
Values 45 percent, 35 percent and 20 percent come from misreading the question or from directly using the given failure percentages without applying inclusion exclusion and complement correctly. Only 40 percent matches the count of students who pass both subjects.

Common Pitfalls:
Common mistakes include adding all three percentages 35, 45 and 20 or subtracting wrongly. Some candidates also confuse the meaning of failing both with passing both. Always use the standard formula for two sets and then take the complement for those who pass both.

Final Answer:
40 percent of the students pass in both Hindi and English.