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# Profit/Loss question

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Profit/Loss question [#permalink]  25 Nov 2010, 08:20
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Question Stats:

49% (05:06) correct 49% (01:19) wrong based on 2 sessions
A dealer offers a cash discount of 20% and still makes a profit of 20% when he further allows 16 articles to be sold at the cost price of 12 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
a) 100%
b) 80%
c) 75%
d) 66+2/3%
e) 55%
[Reveal] Spoiler: OA
Manager
Joined: 08 Oct 2010
Posts: 216
Location: Uzbekistan
Schools: Johnson, Fuqua, Simon, Mendoza
WE 3: 10
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Kudos [?]: 103 [0], given: 974

Re: Profit/Loss question [#permalink]  25 Nov 2010, 08:37
Here is an official explanation of solution method from "Math Question Bank For GMAT Winners" at www.my-gmat.com:

Let the CP (cost price) of the article be \$x, since he earns a profit of 20%, hence SP (selling price)=1.2x.

Loss=[(16-12)/16]*100=25%

His selling price=SP*0,75
Now--> SP*0.75=1.2x
SP=1.2x/0.75=1.6x
This SP is arrived after giving a discount of 20% on MP (marked price).
Hence --> MP=1.6x/0.8=2x --> it means that article has been marked 100% above the cost price.

Can somebody can suggest an alternative solution method with a better explanation?!
I appreciate your help +KUDOS for you!
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Re: Profit/Loss question [#permalink]  25 Nov 2010, 16:50
2
KUDOS
feruz77 wrote:
A dealer offers a cash discount of 20% and still makes a profit of 20% when he further allows 16 articles to be sold at the cost price of 12 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
a) 100%
b) 80%
c) 75%
d) 66+2/3%
e) 55%

I have explained the Mark up - Discount - Profit relation here: http://gmatclub.com/forum/discount-problem-104001.html#p810682

This gives us the formula (1 + m/100)(1 - d/100) = (1 + p/100)
(1 + m/100)(1 - 20/100) = (1 + 20/100)
m = 50
So mark up was 50% in a situation where 12 articles were sold and charged for. i.e. effective mark up turned out to be 50% though his actual mark up was higher since he gave away 16 articles for the cost of 12.

Lets say the cost price of each of the 16 articles was \$1. Then total cost price was \$16 and effective markup was 50% higher on \$16 i.e. 16 + 8 = \$24. So he charged \$24 from the customer. This must have been the marked price on 12 articles. So each article must have a marked price of \$2 i.e. a mark up of 100%

It is definitely a tricky question. If any parts of the solution are unclear, ask.
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Re: Profit/Loss question [#permalink]  26 Nov 2010, 03:13
1
KUDOS
In the case of cost/selling/discount stuff problems, just keep ur brain cool and for any problem, note down the below 5 things first.
These 5 points will take u further, I swear.

1) C=The actual price = the COST PRICE. è hoe much did it cost to the seller to get that product into his shop.
2) S=selling price è what is the price that he is selling the product for. Hence if S>C è profit and if S<C è Loss.
3) X=|S-C|, difference (profit/loss) he made by removing the \$30, for example, sticker and pasting \$40 sticker. After all it is his shop and the product (the ball) is in his shop (court)
4) D=the cheating, but cleverly calculated, discount after he made the changes as specified in point3.
5) GOLDEN POINTS: THE DISCOUNT IS ALWAYS ON “S” – THE SELLING PRICE and THE profit/loss IS ALWAYS ON “C” – THE ACTUAL/COST PRICE

Coming to the original qtn:
Qtn= How much percent above the cost price were his articles listed – this is point 3 above, i.e. asking for X but in terms of percentage.
Hence,the simplified question is à what percent of C is X è X/C * 100 = S-C/C *100 è (S/C – 1) * 100

Given.
Discount of 20% = 1-1/5 = 4/5 times S (as per point5)
Profit of 20% = 1+1/5 = 6/5 TIMES C (as per point5)

Discount of 20% MADE Profit of 20% ( a clever seller, isn’t he)
Hence
New SSelling price = (4/5)S

Not only this. Further more.
he further allows 16 articles to be sold at the cost price of 12 articles to a particular sticky bargainer
 He further reduced the selling price by 12/16
 New S = (12/16)(4/5)S

(12/16)(4/5)S give the profit of (6/5)C
 (12/16)(4/5)S = (6/5)C
 S/C = 2
As the simplified question is à what percent of C is X è X/C * 100 = S-C/C *100 è (S/C – 1) * 100

Answer = (2-1) * 100 = 100%
Or u from S=2C, we can simply say the clever seller has removed the \$30 (i.e C), for an example, sticker and pasted the \$60 (i.e S=2C) sticker.
 100% over the cost price is listed

Regards,
Murali.
Re: Profit/Loss question   [#permalink] 26 Nov 2010, 03:13
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