Question 887033: A man fixed the selling price of his goods at a profit of 10%. while selling his goods he by mistake gave some commission and there was a loss of 1%. what percent was the commission.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
to make a 10% profit, the selling price has to be 1.10 * the cost.
to make a loss of 1%, the selling price has to be .99 * the cost.
the difference in the selling price is 1.10 * the cost - .99 * the cost = .11 * the cost.
.11 * the cost divided by 1.10 * the cost = .11 / 1.10 = .10 which is equal to 10%.
the commission had to be 10%.
let's put this in numbers so you can see how it works.
the cost is 100 dollars.
to make 10% profit, the selling price is 110 dollars.
if he sells at 110 dollars and gets to keep it all, then the profit is 110 - 100 = 10 dollars which is equal to 10% of the cost of 100 dollars.
but, he gives out a 10% commission by mistake.
10% of 110 dollars is equal to 11 dollars.
instead of netting 110 dollars, he now nets 99 dollars because he gave out a commission of 11 dollars on the sale by mistake.
the profit is 99 dollars - 100 dollars equals -1 dollars.
-1 dollars divided by 100 dollars is equal to a profit of -.01 which is equal to a profit of -1% of the cost.
a profit of -1% of the cost is the same as a loss of 1% of the cost because negative profit is equal to loss.
the solution to the problem is that the commission was 10% of the selling price.
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