Question

9. In a city 42% of people read newspaper A,51% read paper B,68% read paper C , 30% read A and B,28% read B and C , 36% read A and C , 8% do not read any of the three.Find the percentage of people who read only one newspaper..??​

Answer 1

Answer:

Let total numbers of people be 100, So for newspapers

n(A)=42,n(B)=51,n(C)=68,n(A∩B)=30

n(B∩C)=28

n(A∩C)=36

Also given, n(

A∪B∪C)

=8

n(A∪B∪C)=100−n(

A∪B∪C)

=100−8=92

Also,

n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

92=42+51+68−30−28−36+n(A∩B∩C)

n(A∩B∩C)=25

Now,

People who read only one paper =n(A)+n(B)+n(C)−2n(A∩B)−2n(B∩C)−2n(A∩C)+3n(A∩B∩C)

=42+51+68−60−56−72+75=48