Question 166

In a class consisting of 100 students, students have the option of registering for three sports (cricket, football and hockey), and each student can register for one, two or all three sports. Number of students playing all three sports is equal to the number of students playing exactly two sports and both of them are equal to half the number of students playing only one sport. What was the total number of registrations?

Solution

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Let: 
x = number of students playing exactly one sport

y = number of students playing exactly two sports

z = number of students playing all three sports

We are given, z=y and x=2z

We know that, x+y+z=100
(2z)+(z)+(z)=100

z=25

Number of registrations will be, 
x+2y+3z
2z+2z+3z=7z

7z=175

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