let us consider following problem:

Roger sold a watch at a profit of $10$%. If he had bought it at $10\%$ less and sold it for $13$ dollar less,then he would have made a profit of $15$%. What is the cost price of the watch?

suppose that price of watch is $x$ dollar, $profit=sell -cost $

so let us denote price of watch by $x$,then if he would buy it $10$ less,then cost of this would be $x-0.1*x=0.9*x$, and if it sold $13$ dollar less,then sold price would be $x-13$, profit is $15$%,then it would be $0.15*x$ right? or we have


but it makes negative equation like $13=-0.05*x$,so what is my mistake,how can i used information like Ronger sold watch at a profit of $10\%$? Thanks in advance

  • $\begingroup$ Your mistake is not using that bit of information about the profit. If he paid $x$ for it, then he sold it for $(1.1)x$, not $x$. $\endgroup$ Aug 9, 2013 at 13:14
  • $\begingroup$ could anybody help me or delete post? $\endgroup$
    – giorgi
    Aug 9, 2013 at 14:00

2 Answers 2



Let Roger has bought the watch at $100x$ dollar

So, the current selling price $=110x$ dollar

If he had bought it at $10$% less, the buying price would have been $=90x$ dollar

If he had sold it for $13$ dollar less, selling price $=110x-13$ dollar

So, $$90x \left(1+\frac{15}{100}\right)=110x-13$$

  • $\begingroup$ i did not understand ,could you be a little more detailed? $\endgroup$
    – giorgi
    Aug 9, 2013 at 13:22
  • $\begingroup$ let take please with numbers $\endgroup$
    – giorgi
    Aug 9, 2013 at 13:23
  • $\begingroup$ @giorgi, unless otherwise specified, the selling price is always based on the buying price. Just put $x=1$ or any positive value for that matter in my answer if you are interested in concrete example $\endgroup$ Aug 9, 2013 at 13:25
  • $\begingroup$ so let us started it like this,suppose that selling price is $x$ ok? $\endgroup$
    – giorgi
    Aug 9, 2013 at 13:26
  • $\begingroup$ if he made profit $10$,it means that cost price is $0.9*x$ right? $\endgroup$
    – giorgi
    Aug 9, 2013 at 13:28

We have costs $c$ and sell price $p$. We know that he had $10\%$ profit, so $$p-c=0.1c$$ On the other hand, $$(p-13) - 0.9c = 0.15\times0.9c$$ Can you take it from here?


On the calulation of profit:

Profit is the difference between the selling price of the good and costs to create this good. In our case the costs are price of watch when it was bought. So, if the agent of the market buys a good for $p_{buy}$ and then resells it for $p_{sell}$, then the absolute profit is $p_{sell}-p_{buy}$. If we want to calculate our profit in percent, then we take them relatively to the costs (it's logical, because they represent our starting money). We have then the formula for relative profit $$\frac{p_{sell}-p_{buy}}{p_{buy}}\times 100\%.$$

As a numerical example, say you spend $100$USD to purchase a bottle of wine (quite a wine, I must say). You let it age for a couple of years and resell it for $120$USD. Your absolute profit is $$120USD-100USD = 20USD,$$ and your relative profit is $$\frac{120USD-100USD}{100USD}\times 100\%=20\%.$$

  • $\begingroup$ i have thought differently,if he made from the beginning $10$ percent profit,and if he would change something and would made $15$ % profit,thus it m means that could use $5$ percent in our equation? $\endgroup$
    – giorgi
    Aug 9, 2013 at 13:18
  • $\begingroup$ it should be $0.1*p$ right?suppose $100$ and $90$,where $100$ price,$90$ cost $\endgroup$
    – giorgi
    Aug 9, 2013 at 13:19
  • $\begingroup$ @giorgi Profit is calculated with respect to the price paid to buy, not price he sold it for. In your example the profit is $100/90 -1 \sim 11\%$. $\endgroup$ Aug 9, 2013 at 13:31
  • $\begingroup$ @giorgi you can't really use those $5\%$, see my comment above. $\endgroup$ Aug 9, 2013 at 13:32
  • $\begingroup$ sorry how?how is profite calculated $\endgroup$
    – giorgi
    Aug 9, 2013 at 13:44

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