In an examination, 42% of students failed in Hindi and 52% failed in English. If 17% failed in both of these subjects, the percentage of students who passed in both subjects is :

1. A

   23%

2. B

   27%

3. C

   34%

4. D

   40%

Appeared in: AIIMS Delhi NO - 2017

Explanation

• The core task is to find the percentage of students who passed both subjects, which is the complement of the group that failed in at least one subject.
• The percentage of students who failed in at least one subject is calculated using the inclusion-exclusion principle: Total Failed = (Failed in Hindi) + (Failed in English) - (Failed in Both).
• Applying the formula: 42% + 52% - 17% = 77%. This is the percentage of students who failed in one or both subjects.
• To find the percentage who passed both, subtract the total failed percentage from 100%: 100% - 77% = 23%.

Why Other Options Were Wrong

• Option B: This is an incorrect value likely resulting from a miscalculation. It does not correspond to a specific logical error in the set theory application.
• Option C: This is an incorrect value likely resulting from a calculation error. It does not align with the correct application of the inclusion-exclusion principle.
• Option D: This result (40%) is obtained by incorrectly calculating the total failed students. It adds only those who failed exclusively in one subject (25% in Hindi + 35% in English = 60%) and subtracts from 100%. This method erroneously omits the 17% who failed in both from the total count of failed students.

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 Percentages as background academic context rather than a clinical decision trigger.
• While not a clinical question, the logical reasoning and data interpretation skills are essential for nurses.
• Understanding set theory is fundamental for interpreting statistical data in nursing research, epidemiology, and public health reports.
• This type of calculation helps in analyzing patient demographics, comorbidity rates, and treatment outcomes where overlapping conditions or risk factors exist.

How to Approach the Question

• Identify the given percentages: % failed in subject A (42%), % failed in subject B (52%), and % failed in both A and B (17%).
• Recognize that the question asks for the percentage who passed both subjects. This is the opposite (complement) of failing in at least one subject.
• Calculate the total percentage of students who failed in at least one subject using the inclusion-exclusion principle: Total Failed = %A + %B - %(A and B).
• Plug in the values: 42% + 52% - 17% = 77%.
• Subtract the total failed percentage from 100% to find the final answer: 100% - 77% = 23%.

Concept Tested & Keywords

• Concept Tested: Set Theory and Percentages
• Stem keywords: percentage, failed in Hindi, failed in English, failed in both, passed in both subjects
• Lead-in keywords: the percentage of students

Question ID

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