Sets

 

Model Question 

Verbal Problems Related to sets 

Some Solved Problems 

2.   In a survey of 75 people, it was found that 40 liked to drink tea only and 8 liked to     drink tea and coffee both. The number of people who liked to drink tea was three     times the number of people who liked to drink coffee. By using a Venn-diagram, find     the  number of people who liked to drink coffee only and who didn't like to drink any     of both drinks.

3.   In a survey of a group of 180 students, 50 students say to like cricket game only, 30 students say

to like basketball game only and 50 students say do not like both games.

(i)       Represent the above information in a Venn diagram.

(ii)      Find the ratio of the students who like cricket game and basketball game.

Soln: Let C and B represent set of students who like cricket game and basketball game respectively, x be the     number of students who like both games and U be the universal set. Then

         n_o(C) = 50, n_o(B) = 30

4.    In a group of 50 students, 20 like only Maths and 15 like only Science. If the number of students who do not like any of the two subjects is double of the number of students who like both subjects, find the number of students who like at most one subject by using a Venn-diagram.

Soln: Let M and S represents the set of students who like Mathematics and Science respectively and let U be   the universal set. Then n_o(M) = 20, n_o(S) = 15, n(U) = 50

         Let n(MÇS) = x, then