# Was it an even deal for me?

I sold a watch to Joanne at $\$20$profit. After a couple of days, Joanne sold the same watch back to me at$\$20$ profit. Was it an even deal for me?

If not, how could I compute the loss or gain incurred (by me) in this whole deal?

Question before:

TITLE: Computing the total loss incurred in selling a an item (at profit) and then buying it back (at loss)

I bought a book for $\$60$.Then I sold it off to a friend for$\$70$.But after a while I felt sorry that I sold it and bought it back for $\$80$.How much loss did I incur? This is similar to I sell the object to a person at$\$10$ profit and then the person sold it back to me at $\$10$profit,I understand that I am incurring loss in the deal but how to compute the percentage loss or the loss itself? Reason for the change: There were some comments indicating that the question/title is not be properly stated and will probably reduce people's tendency to want to deal with it, hence I attempted to make it more compact and to the point but unfortunately, in the process of editing I might have changed the question to a degree that is not intended in general. My apologies to all for this inconvenience. To maintain the consistency of @Srivatsan's answer I am keeping the both version. Thanks, - It never ceases to amaze me how it's possible that people don't even spend the two seconds it takes to proofread at least the title of the question before posting. Aren't you at all worried that this bad impression will reduce people's tendency to want to deal with your question? – joriki Nov 14 '11 at 16:08 @joriki: You're OCD about the English language : D (and possibly about any other languages you speak) +1 for pointing out a typo. – Matt N. Nov 14 '11 at 16:14 @joriki:I can't answer for all, but in this case it was a typo. Anyways, I am always open to suggestion and site offers superb edit features so I guess ...:) – Quixotic Nov 14 '11 at 16:16 Completely changing the question after posting it (without leaving any hint that the question has changed) is considered bad form. – Jon Nov 14 '11 at 16:46 @MaX Well, appending the new question to the old is a good idea. You could just leave the question as it is. – Srivatsan Nov 14 '11 at 16:56 show 2 more comments ## 2 Answers New question: It depends on the value of the watch. Unlike money, a watch could have different values for different people, so it is possible that I could buy a watch from you and still both of us could end up happy with the transaction. Suppose that the watch is worth$\$A$ to me, and assume I paid $\$A$for the watch. So the original deal was a no gain-no loss one for me. Then I sold it to Joanne for$\$A + \$20$. Finally I bought it back from her for$(\$A + \$ 20) + \$20 = \$ A + \$40$. So in effect, I paid $\$(A -(A + 20) + (A + 40)) = \$(A + 20)$ for a $\$ A$item. So I made a net loss of$\$20$.

On the other hand, imagine that the watch was worth $\$ (A+100)$to me. (This means that I originally made a$\$100$ profit.) Then I paid $\$(A+20)$for a$\$(A+100)$ item. So I made a net profit of $\$ 80$. Old question: I am assuming that the book is worth$\$60$, so that the initial transaction is a no loss-no gain one. In the act of selling it and buying it back, my friend made a profit of $\$80- \$70 = \$10$; correspondingly I must lose$\$10$. [You can also verify this explicitly. In total, you paid $\$60 + \$80 - \$ 70 = \$70$ for a $\$ 60$item. So you made a loss of$\$10$.]

If you are interested in the percentage loss, that is simple too. You paid $\$ 70$and got back something worth$\$60$. So calculating your loss as a percentage of the true cost of the watch, your loss is $$\frac{\ 70 - \ 60}{\ 60} \times 100 \%.$$

EDIT: My previous answer calculated loss as a percentage of what you pay; now I relate the loss to the value of the watch, which is what it is actually worth.

-
:If it is worth $\$60$then why are we taking the loss percentage in terms of$70? I guess loss percentage is always computed on cost price unless stated otherwise isn't? –  Quixotic Nov 14 '11 at 17:10
@MaX I am actually confused on that point. My first answer was $10/60$ which I changed to $10/70$ because I am not sure to what I should compare to. –  Srivatsan Nov 14 '11 at 17:46
considering my experiences with this kind of problems,I think it should be 60, but I guess somebody else could confirm. –  Quixotic Nov 14 '11 at 17:53
@MaX I am uncomfortable with 60 appearing in the denominator. I will mull over it a bit and get back to you later today, if that isn't inconvenient. –  Srivatsan Nov 14 '11 at 17:55
@MaX I have come round to your view: I now feel I should relate the loss to the true cost of the watch rather than what I pay. I have edited the answer to reflect this. –  Srivatsan Nov 16 '11 at 19:08
For the watch question, we have to determine what the "whole deal" is. If it is just the two transactions with Joanne, you have lost \$20 (her profit). Buying the watch before selling it doesn't matter. If the original purchase is part of the "whole deal", you started with some money and now have the watch less (the original watch price + \$20). Not knowing what the watch is worth, we don't have the information to answer.