Question

An advertising agency finds that, of 170 people,115 use television,110 use radio and 130 use magazines. also,85 use television and magazines , 75 use television and radio ,95 use radio and magazines ,70 use all the three. find (1) how many use only television ? (2) how many use only radio ? (3) how many use television and magazines but not radio?

Answer 1

Let A,B and C are the people who speak Television, Radio and Magazines respectively.

Number of people who use Television n (A) = 115

Number of people who use Radio n (B) = 110

Number of people who use Magazine n (C) = 130

Number of people who use Television and Magazines

n (A ∩ C) = 85

Number of people who use Television and Radio

n (A ∩ B) = 75

Number of people who use Radio and Magazine

n (B ∩ C) = 95

Number of people who use all the three n (A ∩ B ∩ C) = 70

(i) Number of people who use only Radio = 10

(ii) Number of people who use only Television = 25

(iii) Number of people who use Television and Magazine but not radio = 15