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

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?

Solution -

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.