Question

110 members of a sport club play at least one of the games football,basketball and volleyball,if 20 play football,basketball and volleyball.if 20 play football and basketball only,15 play football and volleyball only,x play all three games,2x each play one game,how many play basketball altogether

Answer 1

There’s a bit of ambiguity in the wording, but interpreting it as:

- Total = 110
- Football & Basketball only = 20
- Football & Volleyball only = 15
- All three = x
- Each single-only category (only football, only basketball, only volleyball) = 2x
- Let Basketball & Volleyball only = y (unknown)

Let only-football = only-basketball = only-volleyball = 2x. Then the total is
110 = 3(2x) + 20 + 15 + y + x = 7x + 35 + y,
so y = 75 − 7x.

Total who play basketball = (only-basketball) + (FB only) + (BV only) + (all three)
= 2x + 20 + y + x = 3x + 20 + (75 − 7x) = 95 − 4x.

So the number who play basketball altogether = 95 − 4x. If you know x (the number who play all three), plug it in to get the numeric answer. If you meant some of the given numbers differently, tell me which and I’ll recompute.