In a school examination 80% student passed in English and 85% students passed in Hindi. If 73% student passed in both subjects then what percent of students failed in the both subjects?

1. A

   8%

2. B

   15%

3. C

   17%

4. D

   35%

Appeared in: RML Lucknow - 2021

Explanation

• To find the percentage of students who failed both subjects, first calculate the total percentage of students who passed in at least one subject.
• Use the formula for the union of two sets: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Here, it's Passed(English or Hindi) = Passed(English) + Passed(Hindi) - Passed(Both).
• Substituting the values: 80% + 85% - 73% = 92%. This means 92% of students passed in at least one subject.
• The percentage of students who failed in both subjects is the total (100%) minus those who passed in at least one: 100% - 92% = 8%.

Why Other Options Were Wrong

• Option B: This represents the percentage of students who failed Hindi (100% - 85% = 15%). This calculation is incorrect because it ignores the data for students who passed or failed English.
• Option C: This value does not correspond to any logical calculation based on the provided data. It is likely included as a plausible-sounding but incorrect numerical distractor.
• Option D: This is the result of adding the percentage of students who failed English (100% - 80% = 20%) and the percentage who failed Hindi (100% - 85% = 15%). This is incorrect because it double-counts the students who failed both subjects.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Set Theory and Percentage Calculation as background academic context rather than a clinical decision trigger.
• This question tests logical reasoning and quantitative aptitude, specifically the application of set theory.
• While not a clinical question, the ability to interpret overlapping data and percentages is a crucial skill for nurses when analyzing patient statistics, research data, and public health reports.
• What if? If 75% of students passed both subjects (instead of 73%), the number of students who passed at least one would be 80 + 85 - 75 = 90%, and the number who failed both would increase to 100 - 90 = 10%.

How to Approach the Question

• Identify the given data: Percentage passed in Subject A, Subject B, and both.
• Recognize the question asks for the percentage who failed in both subjects.
• First, find the total percentage of students who passed in at least one subject using the formula: Total Passed = P(A) + P(B) - P(A and B).
• Calculate: 80% + 85% - 73% = 92%.
• The group that 'failed in both' is everyone outside the 'passed in at least one' group.
• Subtract the total passed percentage from 100% to find the final answer: 100% - 92% = 8%.

Concept Tested & Keywords

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

Question ID

Qt-Vv6cpmInMNFtGSBgtl3

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