SOLUTION: 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 commissio

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.

RELATED QUESTIONS
Goods cost a merchant $72. At what price would he mark them so that he may sell them at... (answered by thepelster)

Goods cost a merchant $72. At what price should he mark them so that he may sell them at... (answered by stanbon,josmiceli)

A merchant buys goods at 25% off the list price. He desires to mark the goods so that he... (answered by rfer)

1. A merchant buys goods at 25% off the list price. He desires to mark the goods so that... (answered by Theo)

A trader marked his goods at 20% above the cost price. If he allows his Customer a 10%... (answered by jorel555)

a trader marked his goods at 20% above the cost price if he allows his customer a 10%... (answered by Theo)

A manufacturer sells to a wholesaler at a profit of 20%, the wholesale price to a... (answered by rfer)

1)Shop keeper M sells some goods to N and makes a profit 15% N resells to p at a loss of... (answered by MathLover1,MathTherapy)

Hello! I'd greatly appreciate it if anyone can help me on this deceptively hard (for me,... (answered by vleith,Greenfinch)