70% of the students who joined XCRI last year play football, 75% play cricket, 80% play basketball and 85% play carrom. The minimum percentage of students who play all four games is:
Let '100x' be the number of students who joined XCRI last year.
Let 'a', 'b', 'c' and d be the number of students who play 1 game, 2 games, 3 games and 4 games respectively.Â
Therefore,Â
a+b+c+d = 100x ... (1)
a+2b+3c+4d = 70x+75x+80x+85x
a+2b+3c+4d = 310x ... (2)
By equation (2) - (1)
b+2c+3d = 210x
We have to minimize 'd' for that we have to maximize c. But c $$\leq$$ 100x
At c$$_{max}$$ = 90x, d$$_{min}$$ = 10x
Therefore, we can say that the minimum percentage of students who play all four games = 10%.
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