Question

In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper, 125 families buy Tamil and English newspapers, 17 families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspapers and 3 families buy all the three newspapers. If each family buy atleast one of these newspapers then find

(i) Number of families buy only one newspaper

(ii) Number of families buy atleast two newspapers

(iii) Total number of families in the colony.

Answer 1

Tamil Newspaper buyers n(A) = 275 

English Newspaper buyers n(B) = 150 

Hindi Newspaper buyers n(C) = 45 

Tamil and English Newspaper buyers n(A ∩ B) = 125 

English and Hindi Newspaper buyers n(B ∩ C) = 17 

Hindi and Tamil Newspaper buyers n(C ∩ A) = 5 

All the three Newspaper buyers n(A ∩ B ∩ C) = 3

(i) Number of families buy only one newspaper = 148 + 11 + 26 

= 185

(ii) Number of families buy atleast two news papers = 122 + 14 + 2 + 3 

= 141 

(iii) Total number of families in the colony = 148 + 11 + 26 + 122 + 14 + 2 + 3 

= 326