How much does the owner lose?

Question

A thief stole a $\$100$ from the owner without him knowing. The same thief comes back inside the store $5$ minutes later and spends $\$70$ of the money. The owner then gives him back $\$30$ in change. How much money does the owner lose?

Answer 1

The owner lose $\$100$ compared to if he wasn't robbed.

@mirko is right that after the first line, the other info is irrelevant. Suppose your money is stolen from your bank account today, you will only notice that in the end of the month, you are poorer by $\$100$ no matter how the thief spend the money. In fact, it is not distinguishable if you replace this thief by another customer who spend $\$70$. The $\$70$ that he seems to spend on you can be viewed as he has directly stolen $\$30$ cash and $\$70$ amount of goods directly from you.

For example,

Suppose a person has $\$ 100$ cash while the owner has $\$130 $ cash and $\$70$ worth of goods.

Case $1$: Suppose the person is not a thief, and buy $\$70$ worth of goods. The person has $\$30$ cash and $\$ 70$ goods while the owner has $\$200$ cash.

Case $2$: Suppose the person steals from you and buy $\$70$ of goods later. After the theft and before the trade, the person has $\$200$ while the owner has $\$30$ and $\$70$ worth of goods. After the thief spend the money, he has $\$130$ and $\$70$ worth of goods while the owner has $\$100$.

The owner is poorer by $\$100$ due to the theft incident.

Answer 2

At the end of the sequence the shop owner has to have $\$100$ and the original goods in the shop We don't know the margin on the goods so you don't know the real cost to the shop owner Lets say goods are on knock down at no profit so he has spent $\$70$ on goods and has $\$100$ float . He looses $\$100$ out the till he will have to replace the goods another $\$70$ he gains cash back but loses a further $\$30$ In summary

-$\$140$ goods ( replace the goods )

$+ \$70$ cash from thief returned

$- \$30$ cash given to the thief

$- \$100$ cash stolen by the thief

= $\$200$ In reality he will have to pay tax on the goods sold , not have paid the full amount on the goods purchased. He will then had whole load of excess on insurance claiming the loss of the $100 and operating costs of ordering etc Without the information you cant tell !! LOL

Answer 3

From owner's perspective,

$-100$ (cash, theft)

$+100$ (cash, tendered)

$-70$ (value, goods)

$-30$ (cash, change)

Total = $- 100$

Overall, that's a loss of $\$100$ from the owner.

But if one takes into account that goods are usually marked up by shops, then the owner would have lost an amount less than $\$100$. The difference would be equal to the profit margin on the item.