In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club

Q. In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is  .

(A) 1000

(B) 975

(C) 900

(D) 225

Ans: 900

Solution:

Students in respective clubs,

Only Drama Club = 60,

Only Dance Club = 80

Only Maths Club = 30

Drama Club and Dance Club = 38 + 2 = 40

Dance Club and Maths Club = 10 + 2 = 12

Drama Club and Maths Club = 5 + 2 = 7

Drama Club and Dance Club and Maths Club = 2

Total number of students = 60 + 80 + 30 + 38 + 10 + 5 + 2 = 225

Since 75% of students are not included in any of the clubs. Therefore, Venn diagram consists of only 25 percentage of students in the college.

Let x be total number of students in the college