The clerk asked for $300.
Each man paid $100, making up the $300.
The hotelkeeper then decided to allow a discount for the day,
charging only $250 for the room.
He told the clerk to return $50 to the three men.
The clerk pocketed $20 for himself.
He gave the remaining $30 back to the three men.
Each man took back $10.
Therefore, each man paid $100 - $10 = $90 for the night.
$90 x 3 = $270 + the clerk's $20 = $290.
Question: Where has the remaining $10 gone?
Many people are still trying to work out an answer.
I was caught in this puzzle too. But to explain it, we need to look at the real situation instead of being led into thinking the amounts do not add up.
The hotel keeper charges $250 and the clerk took $20 from the $270, shared by the three men at $90 each. To the hotel keeper, he gave a discount of $50 from the $300 and receives $250; to the three men, the room costs $270. One does not know the others deal, that's all to it.