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

Question

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?

Paul · Answer

A = 3B
Total cost: B + 3B = 4B
gross profit: .8*3B + .2*B
gross profit/total cost =   / 4B
= 2.4B + .2B / 4B
= 2.6B / 4B = .65

lastochka · Answer

I got a slightly different answer:

 A B
Sale 100 20
CGS 50 20

GP 40 4

GP/CGS = 44/70 = 22/35= 62.8%

Any thoughts?

lastochka · Answer

it seems like there's a flaw in my solution, I just can't quite put my finger on it.

boksana · Answer

I've got 65% too, so I wanted just to check with you guys :wink:

ashkg · Answer

I think the selling price(SP) of A is 3 times of B ( and not the cost price)

So the gross profit should be calculated on Cost price(CP).

Let SP of B = 100.
SP of A = 300

CP of A = 300/1.8
CP of B = 100/1.2

total cost = 300/1.8 + 100/1.2

Total gross profit = (300 - 300/1.8) + (100 - 100/1.2 )

% profit = (total gross profit / total cost )*100= 60%

- ash.

Paul · Answer

ashk, your answer intrigues me.

 

Can you explain how you derived this? Also, are you not taking data from gross profit (profit/cost) and applied it to sales price?

ashkg · Answer

If CP is x and profit is 80% on CP , profit = .8x

the SP would be x+.8x = 1.8x

So CP in terms of SP = SP/1.8 = 300/1.8

Similary

for B , CP = 100/1.2 
as profit is 20%.

hope that clears things.

- ash

Paul · Answer

Hmmm, given that B sales price is 20, shouldn't sales price of A be 60$?
 
Also, how did you get CGS(cost of goods sold) 50$ for A and 20$ for B? Am I missing something here?

Paul · Answer

:nice ashk. Are you an accountant? Well, after your explanation, I declare myself birdbrain :lol:

ashkg · Answer

Hi Paul, You have prompted me to post an introduction of myself

Thanks for that, or I would have done that after my exam. Here is the link. https://www.gmatclub.com/phpbb/viewtopi ... 2114#42114 take care, ash.

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

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