In a school, half of students play badminton, one-fourth (1/4th) play volleyball, one-eighth (1/8th) play tennis, one-sixteenth (1/16th) play chess and remaining go for swimming. If the number of students playing volleyball is 160, how many students play chess?

Options

A. 20
B. 40
C. 120
D. 80

Answer

B

Explanation

Let in a school there are .x. number of students. Half of the students play badminton
`=x xx (1)/(2)`
`(1)/(2)` th students play volleyball =`x xx (1)/(4)`
`(1)/(8) ` th students play tennis = `x xx(1)/(8)`
`(1)/(16)` the students play chess =` x xx (1)/(16)`
Students go for swimming
= Total students - (Number of students who play different games )
`= x -((x)/(2) + (x)/(4) + (x)/(8) +(x)/(16))`
`= x -(15x)/(16) = (16x-15x)/(16)`
Students go for swimming =` (x)/(16)`
Number of students play volleyball
From above students play volleyball
`(x)/(4)`
`(x)/(4) = 160 implies x = 160 xx 4 implies x = 640`
Number of students who play chess are `(x)/(16)`
Put value of x here = `(640)/(16)` =40
Number of students who play chess are 40.