# 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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