Here’s a math puzzler I came across elsewhere. Rather than put it in General Questions, I’m putting it here because it would be interesting to get Doper’s responses to it. I did figure it out myself without much difficulty.
A man goes into a store and steals $100 bill from the cash register. He continues to shop and buys $70 worth of merchandise, paying with the $100 bill and gets $30 in change. How much money did the store lose?
I’ll spoiler my answer so as not to unduly influence anyone’s answers and I’ll post the answer later after enough people have given their own answers. There is one correct answer, but I’d like to see other member’s thought processes on this.
The store lost $100. The original bill was returned to the register and didn’t leave with the thief. The thief walked away with $70 of store merchandise and $30 in cash that he scammed from the store with the $100 bill switcheroo.
That’s only true if the store had a limited amount of goods. If it was a well-stocked store with under-utilized clerks and/or stockers, the store would only be out the $30 minus the cost of the goods, i.e. they’d only be out $100 minus the margin on the goods. They can simply reorder the goods and no one will be the wiser.
It’s another story if they are limited-quantity items or they took all of a popular item or it forces extra labor costs.
My answer:[spoiler]The store lost $100 - or, alternatively, $30 of cash and $70 worth of merchandise. I say “alternatively” because there are two ways of looking at it: from the store’s point of view or from the robber’s.
To the robber, he walked into the store with nothing and walked out with $30 cash and $70 worth of merchandise.
To the store, when they reconcile the register at night, they will find themselves short the $100 cash, with no awareness that the merchandise they sold had anything to do with it. They will only see that the register should have had $170 in it but only had $70.[/spoiler]
Stores obviously don’t stay in business by selling goods at the same price they paid for them. So the store will buy a product for fifty dollars and then sell it for seventy dollars. If the item is stolen, do you regard the loss as the fifty dollars the store already paid or as the seventy dollars the store planned on receiving?
Using proper accounting principles, the goods sold would be on the books at their cost price. So the net loss to the shop would be the $30 change plus the cost price of the goods sold.
The store still has the $100 bill. They would have only been short that $100 if the thief had taken it away from the store with him.
Let’s assume for the purposes of this thread that the loss was the merchandise’s retail value. Even though it wasn’t paid for, it was rung up as a transaction and the store would have received $70 if the payment was legitimate.
Negative $51.14. Turns out the robber was detained by mall security seconds after leaving the store, and everything returned. However, the security guard didn’t realize that some of the cash in the robber’s wallet predated the failed heist.
Given that spoilers seem to get unspoiled in quotes (at least in Firefox), I’m not going to bother with them anymore.
But the store doesn’t see it that way. As far as they were concerned they started with (lets say) one $100 bill and three tens. Then, according to their transaction records, a guy came to the counter and gave them a second $100, and they gave him the merchandise and the three tens back. So, in the store’s opinion, they should now have two $100 bills in the register.
When the store reconciles the contents of the register at the end of the day, they will log themselves as being a single $100 bill short. As far as they’re concerned, the transaction was a legitimate one, and legitimately paid for; they have the money from it and everything.
In fact, that’s such a compelling detail that I’m revising my answer: The theft was of $100 cash, period. That’s what was stolen. The fact that the thief later spent some of their ill-gotten gains doesn’t matter at all.
Cash registers don’t total the amount tendered and change given back. All it will show is the total amount of the transactions rung up. When the manager runs the tape and counts the cash, he will see that there is a $30 difference. The merchandise was paid for with the money with which a previous customer gave the store. It paid for only one set of merchandise.
I think this is a good place to post the correct answer, however, I’ll still spoiler it for anyone who wants to continue to answer.
In fact, this part of it will counter your answer.
[spoiler] Another strategy to solve the problem is to break it down into two stores.
Story A
A guy walks into a store and steals a $100 bill from the register without the owner’s knowledge.
How much money did the owner lose? Clearly the answer is $100. The owner is a net -100.
Story B
He buys $70 worth of goods using a $100 bill and the owner gives $30 in change.
How much money did the owner lose? The owner did not lose any money, this is a routine transaction! If the goods are valued at V, the owner is a net +100 – V – 30 = 70 – V.
The story in the riddle is the sum of the two stories. This means the owner’s position is the sum of the position in those two stories. The owner is a net -100 + (70 – V) = -30 – V. That is, the owner lost $30 plus the value of the goods. If the goods are valued at $70, then the owner lost $100.[/spoiler]
Also, if you switch back to the old version of the forums, spoilers will remain unchanged when quoted.
When you reconcile a cash register you take the starting cash in the register plus cash taken in minus cash handed out, and compare that to the cash found in the register at the end of the day. (This is not the same as just adding in all the day’s sales amounts because of non-cash payment methods.) Most registers are going to start the day with some amount of cash in them to give change out of; for simplicity’s sake I assumed that some of this starting cash was stolen. Things don’t change if the cash came to them from another customer’s payment, though; at end of day the reconciliation will still come up a full $100 short. They won’t come up $30 short, because they fully expected that $70 to be there because they have a record of that transaction and thus expect that money to be there.
(I write point-of-sale software for a living, so I know how this works. )
And I disagree that the cost-to-the-store of the item should be considered while accounting for the store’s loss - by that argument you would have to remark that the store gained X amount of money in a scenario where a sale no theft occurred - the profit from the sale was their gain! Except that’s shoddy accounting; profit needs to take into account all costs, not just the simple purchase price of the item. What was the employee paid for his time selling the item? How much does the building cost to rent, power, and heat? And that’s not even getting into the cost of receipt paper, or the depreciation on the register…
(Our software is a full accounting suite, too. :p)
I’m on the $30 loss, defining “lose” as “have it and then don’t have it.” You don’t lose something you expected to have but don’t.
The store had $X. At the end of the story, they have $X-$30. There was a loss of $30.
Their loss in value was $100, absolutely–but the question wasn’t the value of their loss, it was the value of their loss in money. As such, all elements of the story that are not money are irrelevant.
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