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,
englsih and sanskrit 8,
english 26,
sanskrit 48,
sankrit and hindi 8,
no launguage 24.
find how many students were studying: (1) hindi
(2) english and hindi

Answer 1

Answer in attachment. There are other ways to solve it, but it's one of the easiest ways to do it. Also, please use your mind while finding out the values. Hope it helped.

Answer 2

Number of students studying Hindi is 18

Number of students studying Hindi and English 3.

Solution:

Let the alphabet E, H and  S states that the set of students who are studying English, Hindi and Sanskrit are respectively

Again let U denote the total number of students i.e. , n(U) = 100

The number of English studying students n(E) = 26

The number of Sanskrit studying students n(S) = 48

The number of English and Sanskrit studying students n(E ∩ S) = 8

The number of Sanskrit and History studying students n(S ∩ H) = 8

By intersection of English Hindi and Sanskrit we can find the value of n(E ∩ H ∩ S) = 3

The number of students studying English only = 18

The number of students studying no language = 24

The number of students studying Hindi only  = {100 - (18+5+3+5+35)} - 24

                                                                           = 100 - 66 - 24

                                                                           = 100 - 90

                                                                           = 10

The number students studying Hindi = 10 + 3 + 5 = 18.  

The number students studying Hindi and English is = 3.