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# a store sold A at a price three times as much as B. The

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a store sold A at a price three times as much as B. The [#permalink]

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30 Nov 2006, 16:36
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

.a store sold A at a price three times as much as B. The gross profit of A is 80% of the price that the store paid for A. The gross profit for B is 20% of the price that the store paid for B. what percent is the total gross profit of the total amount that the store paid for both A and B?
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pV

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30 Nov 2006, 17:32
Paayal wrote:
.a store sold A at a price three times as much as B. The gross profit of A is 80% of the price that the store paid for A. The gross profit for B is 20% of the price that the store paid for B. what percent is the total gross profit of the total amount that the store paid for both A and B?

I may have overcomplicated it but here goes:

Let x = price the store paid for A
Selling price of A = 1.8x
Selling price of B = 1/3 of A = 0.6x

Selling price of B = 120% of price paid for B or 1.2B or 6/5B
Price store paid for B = 5(0.6x)/6 = 0.5x

Gross profit of A = 1.8x - x = 0.8x
Gross profit of B = 0.6x - 0.5x = 0.1x

Total gross profit = 0.8x+0.1x = 0.9x
Total amount store paid for A+B = x+0.5x = 1.5x

% of total gross profit from A+B over amount paid for A+B=
100(0.9x/1.5x)
= 60%

OA?
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30 Nov 2006, 18:39
I got 60%. good explanation.

Last edited by tennis_ball on 30 Nov 2006, 20:58, edited 1 time in total.
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30 Nov 2006, 19:18
What is your working tennis ball?
VP
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30 Nov 2006, 20:59
What is your working tennis ball?

sorry. i rushed my calculation just now. I get 60% too.
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01 Dec 2006, 14:03
Not sure what is wrong with this, I get 65%

x = PRICE OF B and 3x = PRICE OF A

Picking numbers x = 100

B Profit Margin of 20% means that the profit for B = 20
A Profit Margin OF 80% mean that the profit for A at a price of 300 (3x) = 240

Total combined selling price is 100 + 300 = 400
Total combined profit is 20 + 240 = 260

The combined profit margin 260 / 400 = 26 / 40 = 13 / 40 = 6.5 / 10 = 65%
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01 Dec 2006, 15:31
lfox2 wrote:
Not sure what is wrong with this, I get 65%

x = PRICE OF B and 3x = PRICE OF A

Picking numbers x = 100

B Profit Margin of 20% means that the profit for B = 20
A Profit Margin OF 80% mean that the profit for A at a price of 300 (3x) = 240

Total combined selling price is 100 + 300 = 400
Total combined profit is 20 + 240 = 260

The combined profit margin 260 / 400 = 26 / 40 = 13 / 40 = 6.5 / 10 = 65%

what percent is the total gross profit of the total amount that the store paid for both A and B
The question is asking for ratio of profit to Cost Price for the store
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01 Dec 2006, 16:02
lfox2 wrote:
Not sure what is wrong with this, I get 65%

x = PRICE OF B and 3x = PRICE OF A

Picking numbers x = 100

B Profit Margin of 20% means that the profit for B = 20
A Profit Margin OF 80% mean that the profit for A at a price of 300 (3x) = 240

Total combined selling price is 100 + 300 = 400
Total combined profit is 20 + 240 = 260

The combined profit margin 260 / 400 = 26 / 40 = 13 / 40 = 6.5 / 10 = 65%

Your mixing up buying/selling price and % profit. For example, selling price of A at 300 = cost + 80%

So if you wanted to calculate the price the store bought A at then it would be (let x = price store paid for A) 180% of x = selling price of A
or 9x/5 = A Therefore x = 5A/9 ----> x = 5*300/9 = 166.66.......
01 Dec 2006, 16:02
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