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. 

Therefore, 

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%.