In a library, among 150 students, 83 read novels, 69 read poetry, and 28 read neither. How many read both?
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Answer and explanation
Correct answer: 30
The number who read at least one of the two types is 150 − 28 = 122, because 28 students read neither. Let N be the novel readers and P the poetry readers. By inclusion-exclusion, n(N ∪ P) = n(N) + n(P) − n(N ∩ P). Therefore 122 = 83 + 69 − n(N ∩ P), so n(N ∩ P) = 30. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
The number who read at least one of the two types is 150 − 28 = 122, because 28 students read neither. Let N be the novel readers and P the poetry readers. By inclusion-exclusion, n(N ∪ P) = n(N) + n(P) − n(N ∩ P). Therefore 122 = 83 + 69 − n(N ∩ P), so n(N ∩ P) = 30. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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