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Question

In a survey of 100 students the number of students studying various languages is found as : English only 18, English but not Hindi 23; English and Sanskrit 8; Sanskrit and Hindi 8, English 26, Sanskrit 48 and no language 24. Find
(1) How many students are studying Hindi?
(2) How many students are studying both English and Hindi?

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Solution

Let denotes the set of surveyed students.
Let E,H and S denotes the set of students who are studying English, Hindi and Sanskrit respectively.
Then, n(U)=100
n(E)=26
n(S)=48
n(ES)=8
n(SH)=8
From the Venn-diagram, it is clear that
n(EHS)=3
The number of students who study English only =18
Number of students who study no language =24
Number of students who study Hindi only =[100(18+5+3+5+35)]24
=1006624
=10090
=10
Number of students who study Hindi =10+3+5
=18
And Number of students who study English and Hindi =3


1091023_1193277_ans_9eb5bdaed90c4a32be42d532f74764f9.png

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