A school has 100 students and every student plays either cricket or football or both. The number of students who play cricket is twice the number of students who play football. Also, the number of students who play only cricket is three times the number of students who play only football. The number of students who play both cricket and football is, therefore :
This questions was previously asked in
EPFO EO AO 2023
Explanation:
Let's solve this step-by-step:
1. Let the number of students who play only football be x.
2. Then, the number of students who play only cricket is 3x because it's three times the number of only football players.
3. Let the number of students who play both sports be y.
4. Total students playing cricket: 3x + y.
5. Total students playing football: x + y.
Given that the number of cricket players is twice that of football players:
3x + y = 2(x + y)
Solving the equation: x = y
The total number of students is given as 100: 3x + x + y = 100
4x + y = 100
Since x = y, replace y with x:
4x + x = 100
5x = 100
x = 20
Therefore, y = 20.
So, the number of students who play both sports is:
- Correct Answer: 20
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By: Babita