# A loss and gain problem

This is a very simple but confusing puzzle.

A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase.

The lady gives him a $1000$ rupee note.

The shopkeeper has no change, so he goes next door to another shopkeeper to get change for the $1000$ rupee note. He keeps $200$ for himself and returns $800$ to the customer.

Later, the second shopkeeper from next door comes back with the $1000$ rupee note with a stamp on it saying "counterfeit" and takes his money back.

How much loss does the first shopkeeper face?

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Indeed that puzzle is phrased confusingly. What does it even mean? Duplicate? –  dfeuer May 30 '13 at 18:06
that is fake currency notes –  iostream007 May 30 '13 at 18:08
I think the lady purchased an item worth 200 with a 1000 bill. The shopkeeper makes the correct change, later to find out that the bill was counterfeit? –  Mark May 30 '13 at 18:13
so at selling lady and shopkeeper are OK but that 1000rs will've to given by shopkeeper and this is lOSS –  iostream007 May 30 '13 at 18:17

The shopkeeper hasn't suffered any loss until the next shop's owner comes over and demands his 1000 rupees back. The shopkeeper hasn't gained anything either, since his profit margin is zero.

Thus, after he reimburses the next shop's owner, he's out 1000 rupees.

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since shopkeeper selling good with zero profit so $200$rs of good selling is not his profit.so when he return 1000 to his neighbor shopkeeper he is in LOSS of $1000$rs. People thinks its answer will be 800.

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Try to explain this to the IRS :) The good part of this question is: Reading comprehension. I like this question and will upvote it! –  imranfat May 30 '13 at 18:11
IRS? what is this? –  iostream007 May 30 '13 at 18:13
@iostream007: The Internal Revenue Service, the US national tax authority. –  Ross Millikan May 30 '13 at 18:15
This is correct. It is simple if you just focus on what he had at the start of the day, which was the goods +1000 rs, and what he had at the end of the day, which was nothing. Since he received nothing (except a fraudulent note) he is out that much. –  Ross Millikan May 30 '13 at 18:18
ok i didn't get that was joke :P –  iostream007 May 30 '13 at 18:18

It's $1200$ guys.. how

once the neighbour asks he gives him back $800$ of his own money plus $200$ what he kept from the change which makes the total loss $1000$ and he lost the goods which cost him $200$ so the answer is $1200$.

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Why post two answers? Why not edit your previous one? –  Willie Wong Jul 2 '13 at 14:33
@Astute: You should not count both goods and Rs. 200 as loss. Because he has only one of them at any time. –  Sai Manoj Kumar Yadlapati Jan 16 '14 at 16:00
no buddy , its 1000 only –  Hussain Akhtar Wahid 'Ghouri' Nov 24 '14 at 7:55

I think the answer will be 2000, considering the lost goods as well: goods worth(zero profit)= 200 change returned= 800; total worth given to customer=1000 (because customer's note value is 0) later 1000 given back to neighbour: thus 1000+1000

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This is right answer. Shop keeper lost (200(goods)+800(change he gave back to lady) ) + 1000 (change from other shop keeper). –  pramodc84 Oct 8 '13 at 9:10
the 1000 that he returned, he received from the second shopkeeper, so actually the loss is only 1000. –  Sumit Jain Dec 1 '14 at 6:36

This is the flow of money had the exchange been genuine. Click to expand.

1. Everyone is at zero standing, meaning no net money flows have happened.
2. The shopkeeper gives the item worth 200 to the customer and receives 1000 in return, but hasn't given change yet. Hence he is 800 up, the customer is 800 down. No net change on the creditor.
3. The shopkeeper changes his 1000 for an 800 and 200. No net change on anybody.
4. The shopkeeper gives the 800 worth of change to the customer. All of them have 0 net flow again.

Now, because the 1000 is counterfeit, we just remove the 1000 from the diagrams. We literally just delete the 1000, and then recalculate the standings. Click to expand.

1. Everyone is still at 0 standing.
2. The shopkeeper gives an item worth 200 to the customer and receives nothing, hence he is 200 down and the customer 200 up.
3. The shopkeeper gets 800 and 200 from the creditor in exchange for the fake bill, hence he is 800 up. The creditor is 1000 down since he lost that much but got thing in return.
4. The shopkeeper gives the customer their change of 800, bringing the shopkeeper to 0 and the customer to 1000.
5. The creditor comes back and takes his 800 and 200 again. This brings the creditor back to 0, and the shopkeeper down by 1000.

So the net loss is 1000.

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for simplicity dont consider other shopkeeper because he get money what he gave. again consider shopkeeper has 800 rs with him and 200 rs good == 1000 initial balance now he gave 200 rs good and 800 rs to lady in returs lady give 1000 rs duplicate note means she gave nothing to him it is equivalent to shopkeeper give 1000 rs free to lady means last balance to him = 0 so toatal loss = initial - final = 1000 - 0 = 1000 Lady (Goods(200) + 800) Shopkeeper (200 (that he kept with him) - 1000 (that he paid to the next shopkeeper)

The shopkeeper has value of goods already (Rs. 200 he kept). (Next shopkeeper has paid on the lady's behalf in this situation)

So the total loss is 1000(to the next shopkeeper) + 800 (to the lady)

=1800

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The shopkeeper lost 200 worth of goods, plus 800 worth of money, which totals to 1000.

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The easiest way to solve this problem is to ignore the counterfeit bill until the end. Instead, assume the shopkeeper's neighbor comes back the next day to make change himself. Only after making change does the shopkeeper notice the counterfeit.

1. Customer gives shopkeeper 1000rs note. Shopkeeper is +1000.
2. Shopkeeper gives neighbor 100rs note. Receives 1000rs change. Shopkeeper is +1000.
3. Shopkeeper gives customer 800rs + 200rs in goods. Shopkeeper is 0.
4. Neighbor comes and asks for change for 1000rs note. Hands shopkeeper same note. Shopkeeper gives change. Shopkeeper is 0.
5. Shopkeeper notices note is counterfeit. Fake 1000rs is worth nothing. Shopkeeper is -1000.
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i) Assuming that the second shop keeper $S_2$ is not doing something fake (saying the bill is fake):

$L=-0+800+x=800+x$

$S_1=+0 -0+1000-800-x+0-1000=-800-x$

$S_2=+0-1000-0+1000$

So shop keeper looses 1000, where $x=200$ and $0$ is the fake bill.

ii) If the the second shop keeper $S_2$ is doing something fake:

$L=-1000+800+x=-200+x=0$

$S_1=+1000 -1000+1000-800-x+0-1000=-800-x=-1000$

$S_2=+1000-1000-0+1000=1000$

In both cases $S_1$ looses $1000$.

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His loss is $1000$.

$$-200_{item}+1000_{fake}-1000_{fake} + (800+200) - 800 + 1000_{fake} - (800+200) = -200_{item} - 800 + 1000_{fake}.$$

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I think it works like this: $200$ is lost as the goods are gone $+$ he gave back real $800$ to the lady which makes a total of $1000$. If he has to return to the neighbour he will return another $1000$, so the total loss would be $2000$.

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Loss is 1800

Got 1000 fake note... changed it from other shokeeper... got real 1000 changed. kept for himself 200 and returned 800...

He got 200 for his good. But returned 800 good Notes to lady.... (Loss)

And again paid 1000 to other shopkeeper from his own pocket... (Loss)

So the loss is 800+1000= 1800

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Actually, the shopkeeper did not loose anything in first transaction while selling his goods. Because, he didn't know that it is fake note, it should be considered genuine. Consider the note as fake in only one transaction. –  Sai Manoj Kumar Yadlapati Jan 16 '14 at 16:08

Total loss is 1800:

1. money changes taken from shopkeeper = 1000
2. goods given to lady = 200
3. money given to lady = 1000 - 200(kept with himself cost of goods) = 800
4. kept with himself cost of goods = 200

Solution : 1+2+3-4 = 1800/-

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He lost 1000 rupees.

If the money was genuine the profit would be zero. (No profit for selling the goods.)

But the money was counterfeit, and hence his loss was the value of the counterfeit money: 1000 rupees.

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## protected by Willie WongAug 7 '13 at 9:20

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