If you are doing this "in theory" then technically you put in infinite number of balls and you take out infinite number, so that's infinity - infinity. Or you can argue, 10*infinity-infinity. You do the math on that and decide.

From my point of view, if you take into the account all the laws of physics, and assume that there really is a mechanism that can put the balls in and take them out in virtually no time, eventually the speed at which this needs to be done will reach light speed, and assuming that you can't go above that, you will no longer be able to put in balls before time reaches noon. Also, if you say that it takes no time to put balls in or take them out then you are saying that motion is done in a period of 0 seconds which is impossible.

So looking at this problem from theoretical point of view, there are a number of solutions, which are all true. But if looking at this problem from realistic point of view, there are many limits on it and that would create a definite answer. You just need to take all the variables into account (i.e. speed of the mechanism that puts balls in/takes them out)