If n(A) = 4x + 6, n(B) = 3x + 9, n(A ∩ B) = 2x + 5, and n(A ∪ B) = 80, find x.
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Answer and explanation
Correct answer: 14
Use the two-set formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given expressions gives (4x + 6) + (3x + 9) − (2x + 5) = 80. Combining terms, 5x + 10 = 80, so 5x = 70 and x = 14. Verification gives n(A) = 62, n(B) = 51, and n(A ∩ B) = 33; therefore 62 + 51 − 33 = 80. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Use the two-set formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given expressions gives (4x + 6) + (3x + 9) − (2x + 5) = 80. Combining terms, 5x + 10 = 80, so 5x = 70 and x = 14. Verification gives n(A) = 62, n(B) = 51, and n(A ∩ B) = 33; therefore 62 + 51 − 33 = 80. 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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