Mike wanted to buy a bike, and he found one he liked at $20, so he bought it. The next day, a friend saw it and offered $30 dollars for it so Mike agreed. He later bought it back for $40. Again someone saw it and offered $50 and again Mike sold it. Mike finally rebought the bike for good for $60. Mike then took it to a bike show where a man told him the bike was worth $40.

Deciding to keep it, did Mike gain or lose money on the transactions? Count the bikes worth in the problem.