The report of one survey of 100 students studying languages Hindi, Bengali and Tamil are as follows. All the three languages 5 students, Hindi and Bengali 10 students, bengali and Tami 8 students,Tamil and Hindi 20 students , Bengali 30 students, hindu 23 students., Tamil50 students. The surveyor who prepared the report was shown the door. Why ?

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