Drunk men at a bar party?

Question

Seven men go to a bar to have a party. The first guy says he'll pay for 1/2 of all the drinks. The second guy says he'll pay for 1/3 of all the drinks. The third says he'll just pay for his own share, or 1/7 of all the drinks. Everybody drinks the same amount, except the one guy that is the designated driver, who doesn't have any drinks at all. Late into the night when the waiter gives them the final bill for $410, the men get into a drunken squabble over the bill because neither 3 or 7 divides into $410. Finally in exasperation the waiter says, "Look, I'm going to add an extra $10 to your bill so you guys can do your math!" This makes the drunken men happy because then the first guy pays $210, or 1/2 of the bill, the second guy pays $140, or 1/3 of the bill, and the 3rd guy pays $60, or 1/7 of the bill, as agreed. The total comes to $410, and so it turns out that the waiter was able to take off that extra $10 from the bill after all. 

So, who got cheated?

Brian · Accepted Answer

Since the designated driver doesn't have any drinks, there are
only 6 men who end up drinking. Since these 6 each drink the
same amount, the third man should be paying for 1/6 of all the
drinks if he is only paying for his share. But since the others
had agreed to the (1/2), (1/3), (1/7) plan the original intention
was that the other 4 men, (or perhaps 3, if we leave out the
non-drinker), were going to cover the remaining (1/42) of the bill.
These 4 guys ended up paying nothing, the (1/7) guy ended
up paying more than (1/7) of the $410 bill but less than the
(1/6)*410 = $68.33 that his drinks actually cost, and the
remaining 2 schmucks paid more than they should have
by $5 and $3.33.

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Drunk men at a bar party?

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