Q46......Sets IIT FOUNDATION CLASS X......................................

Let there be a universal set u. In u, there are 3 sets T,H and E, where T represents members who watch Telugu channel, E represents members who watch English channel and H represents members who watch Hindi channel. Now,let TUH be represented by d, HUE be represented by e and TUE be represented by f. Let HUTUE be represented by g.

Let the set of people who only watch Telugu channel be represented by a, set of people who only watch Hindi channel be represented by b and set of people who only watch English channel be represented by c. (Here the symbol 'U' indicates union of two sets). 

(You can draw the Venn diagram if it is not clear.)

Now, according to the given data,

a+d+g+f=70

b+d+g+e=80

c+f+g+e=95

d=20

e=35

f=15

So, d+e+f=70.

Also, a+b+c+2(d+e+f)+3g=215.

This implies, (a+b+c)+3g= 75___________Eq.1

a+b+c+d+e+f+g=125

This implies, (a+b+c)=55-g___________Eq.2

Replacing from Eq.2 in Eq.1, we get,

55-g+3g=75

2g=20

g=10.

We know g represents the members who watch all the three channels.

So, 10 members watch all the three channels.