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?
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.
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.
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 $1000.$
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.
- Customer gives shopkeeper 1000rs note. Shopkeeper is +1000.
- Shopkeeper gives neighbor 100rs note. Receives 1000rs change. Shopkeeper is +1000.
- Shopkeeper gives customer 800rs + 200rs in goods. Shopkeeper is 0.
- Neighbor comes and asks for change for 1000rs note. Hands shopkeeper same note. Shopkeeper gives change. Shopkeeper is 0.
- Shopkeeper notices note is counterfeit. Fake 1000rs is worth nothing. Shopkeeper is -1000.