If the question asks for the average percentage per month over some specified timeframe (in this case 4 months), you need to first calculate the monthly averages and then average them together (like you did in your first example). The question you're answering in your second method is different. It's "what is the average percentage of redheads in the room over this entire four month period" (or something like that), in which case you take the total number of redheads (4) divided by the total number of people in the room (10) and come up with 40%. The point-in-time element of this question makes it weird though
"The trophy problem has become extreme."