Q3 of 43 Page 16

In competitive exam 50 students passed in English. 60 students passed in Mathematics.40 students passed in both the subjects. None of them fail in both the subjects. Find the number of students who passed at least in one of the subjects?

Given: n(A) = 50, n(B) = 60 and n (A ∩ B) = x = 40

n(A) = number of students who passed in English


n(B) = number of students who passed in mathematics


n (A ∩ B) = number of students who passed both subjects


n (A ∪ B) = number of students who passed in at least one of the subject


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As we know, n (A ∪ B) = n(A) + n(B) - n (A ∩ B)


⇒ n (A ∪ B) = 50 + 60 - 40


⇒ n (A ∪ B) = 110 - 40


⇒ n (A ∪ B) = 70


Hence, the number of students who passed in at least one of the subject = 70


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