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 ?

Let ∩ denotes the set of surveyed students.

Let E, H and S denote the set of students who are studying English, Hindi and Sanskrit respectively.

Then, n (∪) = 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

Number of students who study no language = 24

∴ Number of students who study Hindi only = [100 – (18 + 5 + 3 + 5 + 35)] – 24

= 100 – 66 – 24

= 100 – 90

= 10

∴ Number of students who study Hindi

= 10 + 3 + 5

= 18

and Number of students who study English and Hindi = 3