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: HPSSC - 2015

Explanation

• The problem requires calculating the complement of a union of two sets.
• First, calculate the total percentage of students who failed in at least one subject using the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
• Total failed percentage = 42% (Hindi) + 52% (English) - 17% (Both) = 77%.
• The percentage of students who passed in both subjects is the total (100%) minus the percentage of those who failed in at least one subject.
• Calculation: 100% - 77% = 23%.

Why Other Options Were Wrong

• Option B: This is an incorrect calculation. It might result from incorrectly adding or subtracting percentages without following the set theory formula. For example, 100% - (42% + 52% - 17% - 17%) is not a valid approach.
• Option C: This value is incorrect. It could be the result of a miscalculation, such as adding the two 'only' failed groups (25% + 35% = 60%) and then subtracting it from 100% (40%) and making another error.
• Option D: This value is incorrect. It might be obtained by incorrectly subtracting the sum of individual failure rates from 100% (100 - 42 - 52 = 6) and then making another error.

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.
• While not a clinical question, this type of logical reasoning and calculation is essential for interpreting statistical data in research articles, such as patient outcomes or study demographics.
• Nurses use percentage calculations daily for tasks like medication dosage, IV drip rate calculations, and interpreting lab results.
• What if 17% passed both subjects instead of failing? The question would then be to find the percentage who failed in at least one. In that case, the answer would be 100% - 17% = 83% failed in at least one subject.

How to Approach the Question

• Identify the given percentages: % failed in Subject A, % failed in Subject B, and % failed in both (A ∩ B).
• Recognize that the question asks for the percentage of those who passed both, which is the complement of the group that failed in at least one subject.
• Use the formula for the union of two sets to find the total percentage of students who failed in at least one subject: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
• Calculate the total failed percentage: 42% + 52% - 17% = 77%.
• Subtract the total failed percentage from 100% to find the percentage of students who passed both subjects: 100% - 77% = 23%.
• Select the option that matches your result.

Concept Tested & Keywords

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

Question ID

QZmkOyX8nOnvsFtChM9jUh

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