In a school examination, 90% of students passed in English and 80% of students passed in Hindi. If 75% of students passed in both subjects, then what percent of students failed in both subjects?

1. A

   5%

2. B

   15%

3. C

   17%

4. D

   35%

Appeared in: RML 2023

Explanation

• The problem requires finding the percentage of students who are outside the set of those who passed in either English or Hindi.
• Using the principle of inclusion-exclusion, the percentage of students who passed in at least one subject is calculated as: P(English) + P(Hindi) - P(Both).
• Calculation: 90% + 80% - 75% = 95%. This is the percentage of students who passed at least one subject.
• The percentage of students who failed both subjects is the complement of those who passed at least one: 100% - 95% = 5%.

Why Other Options Were Wrong

• Option B: This value represents the percentage of students who passed in English only, not those who failed in both subjects.
• Option C: This is an incorrect value that does not result from any logical calculation based on the provided data.
• Option D: This is an incorrect value, possibly derived from a misunderstanding of the set theory formula.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Set Theory and Percentages as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of logical and mathematical reasoning is a fundamental skill for nurses.
• Nurses use similar calculations for tasks like interpreting statistical data in research articles, understanding risk percentages for diseases, or calculating medication dosages.
• What if? If 70% of students passed in both subjects instead of 75%, the number of students who passed at least one subject would be 90% + 80% - 70% = 100%. This would mean 0% of students failed in both subjects.

How to Approach the Question

• First, identify the percentages given for each category: passed in subject A, passed in subject B, and passed in both.
• Recognize that this is a set theory problem. The goal is to find the complement of the union of the two sets (students who passed).
• Use the formula for the union of two sets: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). This gives the total percentage of students who passed at least one subject.
• Calculate the value: 90% + 80% - 75% = 95%.
• To find the percentage who failed in both, subtract the result from 100%: 100% - 95% = 5%.
• Double-check your calculations and ensure you are answering the specific question asked (failed in both, not passed in one only).

Concept Tested & Keywords

• Concept Tested: Set Theory and Percentages
• Stem keywords: passed in English, passed in Hindi, passed in both, failed in both, percent
• Lead-in keywords: what percent

Question ID

Qf-zZkcXZFbYAGZPcHlo6V

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