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A dealer offers a cash discount of 20% and still makes a pro [#permalink]
25 Nov 2010, 07:20

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Difficulty:

95% (hard)

Question Stats:

37% (04:07) correct
63% (02:15) wrong based on 92 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?

Re: Profit/Loss question [#permalink]
25 Nov 2010, 07:37

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!

Re: Profit/Loss question [#permalink]
25 Nov 2010, 15:50

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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%

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. _________________

Re: Profit/Loss question [#permalink]
26 Nov 2010, 02:13

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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 SSelling 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

Re: Profit/Loss question [#permalink]
11 Aug 2013, 07:41

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Tricky Question - But the key is to, as always, understand the question inside out

Given

Cash Discount - 20% Profit - 20% Items Sold - 16 Price Sold at = List Price of 12

Assume List price = $10 Total Invoice = $120 -20% Cash Discount = $96 Let cost price of 16 items be x So total cost = 16*x Given the shopkeeper had a profit of 20%

16 * x * 120/100 = 96

or x = $5

Which means his products were listed at $10 which is a 100% markup over $5

Answer A _________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

Re: A dealer offers a cash discount of 20% and still makes a pro [#permalink]
18 Feb 2014, 08:17

1

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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%

Wow! this one one tough one. Let's see

Let's call 'P' the price and 'C' the cost

We have 0.8P = 1.2C

Now we also know that we had an additional (16-12)/16=4/16=3/4 discount on the price