In a group of students 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?
Let U be the set of all students in the group.
Let E be the set of all students who know English.
Let H be the set of all students who know Hindi.
∴ H ∪ E = U
Accordingly, n(H) = 100 and n(E) = 50
n( H U E ) = n(H) + n(E) – n(H ∩ E)
= 100 + 50 – 25
= 125
Hence, there are 125 students in the group.
“Cheery confidence” and “inexplicable hopefulness” are the two phrases which respectively show that the author’s friend knew what he was doing and was absolutely sure that it was good.
(d) Number of students who speak only English = (Number of students who speak English – Number of students who speak both Hindi and English)
= 21 – 10 = 11
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