CSAT 2024

Q. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

a) 15%
b) 20%
c) 25%
d) 35%
Correct answer: b) 20%

Question from UPSC Prelims 2024 CSAT

Explanation : 

In an examination, 80% of students passed in English

Let’s approach this step-by-step:

1) Let’s define our variables:
Let x be the total number of students.

2) We know:
– 80% passed English, so 20% failed English
– 70% passed Hindi, so 30% failed Hindi
– 15% failed both subjects

3) Let’s create a Venn diagram in our mind:
– Let A be the set of students who failed English
– Let B be the set of students who failed Hindi
– The intersection of A and B (A ∩ B) is 15% of x

4) We need to find:
(Students who failed English only) + (Students who failed Hindi only)

5) Students who failed English only:
20% – 15% = 5% of x

6) Students who failed Hindi only:
30% – 15% = 15% of x

7) Total percentage of students who failed in only one subject:
5% + 15% = 20%

Therefore, the correct answer is b) 20%.

 

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