A group of 42 children all play tennis or football, or both sports. The same number play tennis as play just football. Twice as many play both tennis and football as play just tennis. How many of the children play football?
Answers
All Subjects = 10 , Hindi only = 20 & Commerce only = 15
Step-by-step explanation:
Economics E = 125
Hindi H = 100
Commerce C = 145
Economics only = 25
Economics & Hindi = E ∩ H = 30
Economics & Commerce = E ∩ C = 80
Hindi & Commerce = C ∩ H = 60
All subject E ∩ H ∩ C = ?
Economics only = E - E ∩ H - E ∩ C + E ∩ H ∩ C
=> 25 = 125 - 30 - 80 + E ∩ H ∩ C
=> E ∩ H ∩ C = 10
Hindi only = H - E ∩ H - H ∩ C + E ∩ H ∩ C
=> Hindi only = 100 - 30 - 60 + 10
=> Hindi only = 20
Commerce only = C - E ∩ C - H ∩ C + E ∩ H ∩ C
=> Commerce only = 145 - 80 - 60 + 10
=> Commerce only = 15
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A group of 42 children all play tennis or football, or both sports. The same number play tennis as play just football. Twice as many play both tennis and football as play just tennis. How many of the children play football?
Step-by-step explanation:
We will assume:
Each child play at least one game
Children Play Tennis = T
Children Play FootBall = F
Children Play Both = B
Just FootBall = F – B
Just Tennis = T – B
The same number play tennis as play just football
=> F – B = T
Twice as many play both tennis and football as play just tennis
2B = T – B
=> T = 3B
F – B = 3B
=> F = 4B