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A merchant sells an item at a 20% discount, but still makes [#permalink]

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13 Sep 2007, 23:57

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A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

A) 20% B) 40% C) 50% D) 60% E) 75%

C

assume its 100 before discount.
so it was sold at 80 .
still gross profit of 20 means . original cost was 80 *( 100/120) = 200/3

I have explained the concept below from which we derive the following formula. It makes calculations very simple and you don't need to learn up the formula because it will make sense and stick with you once you go through the explanation:

\(( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})\) where m% is mark up %, d% is discount % and p% is profit %.

Using the formula to solve your question: If d = 20 and p = 20, \(( 1 + \frac{m}{100}) * (1 - \frac{20}{100}) = (1 + \frac{20}{100})\) \(( 1 + \frac{m}{100}) * (\frac{4}{5}) = (\frac{6}{5})\) m = 50 Therefore, the merchant had marked up by 50% which would have been his profit had he not given the discount.

Let me explain the concept now. Let us say cost price of an item is $100. I, a merchant, mark it up by 40% and put a tag on it of $140. Now, I have a sale and I offer everything at 10% discount. So something that is marked at $140, will get $14 off and will be sold at $126. The profit I made on the item is $26 (= 126 - 100 (which was my cost price)). This profit is equal to a profit % of 26/100 = 26% (Profit/CP x 100) Note here that my mark up % was 40%, I gave discount of 10% but my profit is only 26%, not 30%. This is because the 40% mark up was on cost price while when I gave discount, I gave 10% on the marked price (which was way more than cost price). The diagram below will make this clearer.

Attachment:

Ques.jpg [ 13.44 KiB | Viewed 38815 times ]

We can make up a quick formula. If m% is the mark up %, d% is the discount % and p% is the profit %, then cost price x ( 1 + m/100) = marked price marked price x (1 - d/100) = selling price which means: cost price x ( 1 + m/100) x (1 - d/100) = selling price We know, cost price x (1 + p/100) = selling price From the 2 equations above, \(( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})\)

In other words, when cost price is increased by m% and then decreased by d%, it is equivalent to increasing the cost price by p%.
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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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06 Jun 2014, 02:37

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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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14 Sep 2015, 13:26

Hello from the GMAT Club BumpBot!

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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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04 Dec 2016, 21:38

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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