Question

In a survey of 100 persons it was found that 28 read magazine A, 30 read magazine B, 42

read magazine C, 8 read magazines A and B, 10 read magazines A and C, 5 read magazines B

and C and 3 read all the three magazines. Find

(i) How many read none of three magazines?

(ii) How many read magazine C only?​

Answer 1

Answer:

Correct option is

A

20

Total number of persons=100

Number of persons who read magazine A=n(A)=28

Number of persons who read magazine B=n(B)=30

Number of persons who read magazine C=n(C)=42

Number of people who read both  magazine A and B = n(A∩B)=8

Number of people who read both  magazine B and C= n(B∩C)=5

Number of people who read both  magazine A and C = n(A∩B)=10

Number of people who read both  magazine A, B and C = n(A∩B∩C)=3

Number of people who read none of the three magazines= n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

n(A∪B∪C)=28+30+42−8−5−10+3

Therefore total number of readers=80

Number of readers who read none of the three magazines= 100−80=20