Let the no of students who play hockey = x
No of students who play football = 2x + 5
No of students who play both hockey and football = 15
ATQ,
x + 2x + 5 -15 = 80
3x - 10 = 80
3x = 90 ∴ x = 30
No of students who play football = 2 × 30 + 5 = 65
Hence, 30 students play hockey, 65 play football and 15 play both.
(i) 65 students play football
(ii) No of students who play football but not hockey = 65 - 15 = 50
(iii) No. of students who play hockey but not football. = 30 - 15 = 15