# A simple yet confusing puzzle - Fake money involved! [duplicate]

A very simple but confusing puzzle.A lady buys goods worth rs.200 from a shop.(Shopkeeper selling the goods with zero profit).The lady gives him 1000 rs note. The shopkeeper gets the change from the next shop and keeps 200 for himself and returns rs.800 to d lady.Later the shopkeeper of the next shop comes with the 1000rs note saying"duplicate" and takes his money back.How much LOSS did the shopkeeper face?

Edit:

Generally concieved answer is 1000rs. But should we not consider the loss from counterfeit currency. If that would be considered as loss then the answer would be 2000. is it not?

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## marked as duplicate by Blue, mau, Lord_Farin, L.G., BelgiJun 13 '13 at 8:43

Yes. It seems like that. And that question doesnt have any accepted answers! –  selvin Jun 13 '13 at 7:44

He starts with 0. She gives him 1000, he gives her 800. Now he has 200. Now the neighbor takes 1000, so he gives the 200 he has and 800 more, for a net loss of 800.

Another way to see this is to look from the lady's perspective. To her, the two shops form a "black box" where somehow she pays in fake (that is, 0) money and receives 800. So 800 had to be lost from somewhere. The neighbor didn't lose any money, so it had to come from the original person.

However, he also lost 200 in supply. So maybe you want to say he lost 1000, because he does not have those items to sell to someone who will give him real money.

You can see this from the lady's perspective as well: in addition to getting 800 she also got 200 worth of supply, which also had to come from the original person.

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And what has happened to the fake note he got from the lady. That is also his potential loss right? –  selvin Jun 13 '13 at 8:26
So wouldnt the loss be 800 in Cash + 200 in goods + 1000 as fake note which he cant use further? –  selvin Jun 13 '13 at 8:28
The note wasn't actually money, though. If the shopkeeper (original) lost 2000, then that means the neighbor had to gain 1000. But the neighbor clearly made/lost nothing. The "potential loss" from the note was actually part of the real loss from his neighbor demanding the money back. –  Eric Stucky Jun 14 '13 at 0:49
Think about it this way: Pretend the note was real for a minute. Then the shopkeeper gained 200, even if the neighbor thinks it's a fake and has him trade 1000 in change back for the (not fake) 1000 note. Okay, so if it was real, the shopkeeper gained 200. Then the fact that the note wasn't real means that he actually gained 200-1000=-800. It doesn't make sense to remove that note's value twice :) –  Eric Stucky Jun 14 '13 at 0:52

The shopkeeper loses $1000$ rupees. Here is a flow chart of each transaction:

$$0\xrightarrow{\text{sold goods}} -200\xrightarrow{\text{borrowed from neighbor}} 800\xrightarrow{\text{change to woman}} 0\xrightarrow{\text{paid back neighbor}} -1000$$

Another way to think about this is total gain/loss for all parties involved. The woman gains $200$ from the goods, and $800$ from the change. There is no gain or loss for the neighbor. Since its a zero sum game, it follows that the shopkeeper loses $1000.$

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