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In a class of 120 students, 100 students like either Hindi or English. 75 students like Hindi and 65 students like English. The students who like neither Hindi nor English mean that they like History. How many students like English subject only?

In a class of 120 students, 100 students like either Hindi or English. 75 students like Hindi and 65 students like English. The students who like neither Hindi nor English mean that they like History. How many students like English subject only? Correct Answer 25

Given,

Total number of students in the class = 120

Number of students who like either Hindi or English = 100

Number of students who like Hindi = 75

Number of students who like English = 65

Calculation:

Here let set A be Hindi and set B be English

A = 75 and B = 65

⇒ A ∪ B = 100

⇒ A ∪ B = 75 + 65 - A ∩ B

⇒ A ∩ B = 140 - 100 = 40

Thus the number of students who like both subjects Hindi and English are 40.

∴ Number of students who like only English subject = 65 - 40 = 25

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