Relation between sales and %profit.

The question is

Quote:

Mr.Cutler usually makes a 45% profit on every radio he sells .During a sale he reduces his margin of profit to 40% whiles his sales increase 10%.What is the ratio of his new total profit to the original profit.

The ans is 44:45

I could solve this problem however the the increase in sales is throwing me off . If i dont consider increase in sales i get 8:9. Is there a relation between increase in sales to the profit earned?

Here is how i did it

Let the radio price be p.

--Now Before the sale.

Selling price = 29p/20)

Profit = (29/20)p - p = (9/20)p

--After Sale Price

Selling price =7p/5

Ratio -

New total profit : original profit = 8:9

Re: Relation between sales and %profit.

Hello, MikeNoob!

You're making hard work out of this problem . . .

Quote:

Mr. Cutler makes a 45% profit on every radio he sells.

During a sale, he reduces his margin of profit to 40% while his sales increase 10%.

What is the ratio of his new total profit to the original profit?

The ans is 44:45

$\displaystyle \text{Suppose that normally he sells }x\text{ radios.}$

$\displaystyle \text{Then his profit is: }\,0.45x\text{ dollars.}$

$\displaystyle \text{During the sale, he sells }\,x + 0.10x \,=\,1.10x\,\text{ radios.}$

$\displaystyle \text{Then his profit is: }\,0.40(1.10x) \,=\,0.44x\text{ dollars.}$

$\displaystyle \text{The ratio is: }\:\frac{\text{new profit}}{\text{old profit}} \;=\;\frac{0.44x}{0.45x} \;=\;\frac{44}{45} \;=\;44:45$

Re: Relation between sales and %profit.

Thanks that was simple :).