Question:
In a survey of 100 students, the number of students studying the
various languages were found to be English only 18, English but not
Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and
Hindi 8, Number of no language 24. Find
i) How many students were studying Hindi?
ii) How many students were studying English and Hindi
Answer:
Let E, H and denotes the set of students who are studying English, Hindi and Sanskrit respectively.
Again let U denotes the set of surveyed students.
Now, n(U) = 100
n(E) = 26
n(S) = 48
n(E ∩ S) = 8
n(S ∩ H) = 8
From the venn-diagram, it is clear that
n(E ∩ H ∩ S) = 3
The number of students who study English only = 18
The number of students who study no language = 24
The number of students who study Hindi only = {100 - (18+5+3+5+35)} - 24
= 100 - 66 - 24
= 100 - 90
= 10
So, the number of students who study Hindi only = 10 + 3 + 5 = 18
and the number of students who study English Hindi = 3
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