In a party of 100 people, 50 person do not prefer Veg, 60 prefer Non-veg and 10 do not prefer either Non-veg or Veg...

Question

A dinner party is to be fixed for a group consisting of 100 persons. In this party, 50 person do not prefer Veg, 60 prefer Non-veg and 10 do not prefer either Non-veg or Veg.

How many people prefer both Veg and Non-veg?

Answer 1

Lets assume A is the set of Veg people and B is the set of Non-Veg People
n(A U B) = 100 - 10 = 90
n(A) = 100 - 50 = 50
and n(B) = 60
Therefore
n(A Inter B) = n(A) + n(B) - n(A U B)
= 50+60 - 90
= 20

So 20 people prefer veg and non-veg both.

Answer 2

no. of person prefer both = x
no. of person prefer chicken(only) = 60-x
no. of person prefer fish (only) = 50-x
then now
60-x+50-x+x=100-10
110+x=90
x=20

Answer 3

veg 50 non veg 40 both 10