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

In a school, half of the students play badminton, one-fourth (1/4th) play volleyball, one-eighth (1/8th) play tennis, one-sixteenth (1/16th) play chess and the remaining go for swimming. If the number of students playing volleyball is 160, how many students play chess? Correct Answer 40

Let the number of total students be ‘X’

Given in the question,

Students playing Badminton = ½ X

Students playing Volleyball = ¼ X

Students playing Tennis = 1/8 X

Students playing Chess = 1/16 X

According to question,

Number of students playing Volleyball = ¼ X = 160

= ¼ X = 160

= X = 160 × 4 = 640

i.e total no of students = 640

Now, substituting the value of x we get,

Students playing Chess = 1/16 X = 1/16 × 640 = 40 (ANS)

Important Points

Similarly, if the other number was asked:

Students playing Badminton = ½ X = ½ × 640 = 320

Students playing Volleyball = ¼ X = ¼ × 640 = 160

Students playing Tennis = 1/8 X = 1/8 × 640 = 80

Remaining = 640 – (320 + 160 + 80 + 40) = 640 – 600 = 40