Discussion

Explanation:

Since 15 failed in both subjects there are 150 – 15 = 135 students who passed in at least one subject.

n(M) = number of students who passed in Maths = 90
n(E) = number of students who passed in English = 65
n(M∩E) = number of students who passed in both Maths as well as English.
n(M∪E) = number of students who passed in at least one of Maths or English = 135

∴ n(M ∪ E) = n(M) + n(E) - n(M∩E)
⇒ 135 = 90 + 65 - n(M∩E)
⇒ n(M∩E) = 90 + 65 – 135 = 20

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∴ Number of students who passed in both the subjects = 20

Hence, 20.

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