Question

1. 40% of the students in a college play basketball, 34% of the students play tennis and the number of students
who play both the games is 234. The number of students who neither play basketball nor tennis is 52%. Find
the student population in the college.
(a) 800
( 1050
(c) 900
(d) 850

Answer 1

Given:

40% of the students in a college play basketball, 34% of the students play tennis and the number of students  who play both the games is 234

To find:

Total students in the college

Solution:

n( basketball) = 40%

n(tennis) = 34%

n(basketball ∪ tennis)' = 52%

n(basketball ∪ tennis) = 100-52 = 48%

we know that:

n(basketball ∪ tennis) = n( basketball)+n(tennis)-n(basketball ∩ tennis)

48% = 40% + 34% - n(basketball ∩ tennis)

n(basketball ∩ tennis) = 74% - 48%

n(basketball ∩ tennis) = 26%

as per the question:

26% = 234

1% = 9

100% = 900

Hence, the total student in the college is 900