Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 12 Mar 2014, 12:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
VP
Joined: 08 Jun 2005
Posts: 1158
Followers: 6

Kudos [?]: 99 [0], given: 0

A merchant sells an item at a 20% discount, but still makes [#permalink]  13 Sep 2007, 22:57
00:00

Difficulty:

5% (low)

Question Stats:

31% (02:06) correct 68% (00:44) wrong based on 19 sessions
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%

Intern
Joined: 14 Mar 2005
Posts: 28
Followers: 0

Kudos [?]: 3 [0], given: 0

regular price = $100 discounted price =$100 - 20% = $80 c + .2c = 1.2c = 80 c = 66.6 if sold at regular price, profit is 100-66.66 = 33.33 33.33/66.66 = 50% (C) Director Joined: 17 Sep 2005 Posts: 933 Followers: 2 Kudos [?]: 17 [0], given: 0 [#permalink] 14 Sep 2007, 08:18 Let the Market Price of the product is MP. Let the Original Cost Price of the product is CP. Selling Price (Discounted Price) = 100%of MP - 20%MP = 80% of MP. ---------------- (1) Profit made by selling at discounted price = 20% of CP -------------- (2) Apply the formula: Profit = Selling Price - Original Cost Price => 20% of CP = 80% of MP - 100% CP => MP = 120CP/80 = 3/2 (CP) Now if Product is sold without any discount, then, Profit = Selling Price (without discount) - Original Cost Price = Market Price - Original Cost Price = MP - CP = 3/2 CP - CP = 1/2 CP = 50% of CP Thus, Answer should be C. Nice question. - Brajesh Director Joined: 08 Jun 2007 Posts: 585 Followers: 1 Kudos [?]: 67 [0], given: 0 Re: Merchant Sells Item Discount [#permalink] 14 Sep 2007, 08:29 KillerSquirrel wrote: 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 if no discount it would have been sold at 100 so profit [100- 200/3] / [200/3 ] * 100 = 50% Manager Joined: 29 Aug 2007 Posts: 112 Followers: 1 Kudos [?]: 0 [0], given: 0 [#permalink] 14 Sep 2007, 13:13 Killersquirrel What is the answer to this question I have spent over 30 mins and still no where Cost = 100 selling price 80 Based on the profit should be negative If he is still making 20 % profit if SP < Cost then it can never be a profit? am I missing something her? VP Joined: 08 Jun 2005 Posts: 1158 Followers: 6 Kudos [?]: 99 [0], given: 0 [#permalink] 14 Sep 2007, 13:34 the OA is (C) The "trick" is to find the original cost ---> C 80-Cost = Profit P/C = 20/100 (80-C)/C = 20/100 80-C = 1/5*C 80 = 1/5*C+C 80 = 6/5*C 400 = 6*C C = ~67 hence ---> 100-67=33 ---> 33/67 = ~50 Director Joined: 30 Nov 2006 Posts: 592 Location: Kuwait Followers: 11 Kudos [?]: 132 [0], given: 0 [#permalink] 14 Sep 2007, 14:03 S: selling price C: cost 0.8S - C = 0.2C --> 0.8 S = 1.2 C --> S = 1.5 C S - C = 1.5 C - C = 0.5 C ANS: C [50%] Senior Manager Joined: 27 Aug 2007 Posts: 257 Followers: 1 Kudos [?]: 8 [0], given: 0 [#permalink] 15 Sep 2007, 07:34 It is C, But took some time to figure out (3-4 mins) Ans: C Math Forum Moderator Joined: 20 Dec 2010 Posts: 2058 Followers: 122 Kudos [?]: 815 [0], given: 376 Re: Merchant Sells Item Discount [#permalink] 05 Jan 2011, 05:48 Ans: C Suppose the cost price as 100. The managed to sold it with 20% profit. Thus, he sold it for 120. And 120 was the discounted rate of 20%. 120 is 80% of 150. So, the marked price was 150, selling at which would incur a good profit of 50%. _________________ ~fluke Intern Joined: 21 Sep 2010 Posts: 17 Followers: 0 Kudos [?]: 1 [0], given: 0 Re: Merchant Sells Item Discount [#permalink] 05 Jan 2011, 11:43 Let the selling price without discount =$x

Cost Price =$y Gross Profits without discount = x-y % of gross profit without discount = (x-y/y)*100 = (x/y -1)*100 With data given we know that: .8x= 1.2y x/y = 3/2=1.5 % of gross profit without discount = (x-y/y)*100 = (x/y -1)*100 = (1.5-1)*100= .5*100=50% Answer C Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4041 Location: Pune, India Followers: 862 Kudos [?]: 3628 [0], given: 144 Re: Merchant Sells Item Discount [#permalink] 06 Jan 2011, 21:45 Expert's post 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 9965 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%. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Director
Joined: 01 Feb 2011
Posts: 774
Followers: 12

Kudos [?]: 75 [0], given: 42

Re: Merchant Sells Item Discount [#permalink]  12 Mar 2011, 07:31

Lets say

Cost - C
List Price - LP
Selling Price - SP

Profit = SP -C

Profit if sold at 80% of LP = (80LP/100)- C = 20C/100 => 2LP = 3C

Profit if sold at LP = (LP-C/C)*100 = 50%
SVP
Joined: 16 Nov 2010
Posts: 1698
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 28

Kudos [?]: 261 [0], given: 36

Re: Merchant Sells Item Discount [#permalink]  12 Mar 2011, 08:46
MP = 100

So SP = 80

SP - CP = 0.2CP

So 80 = 1.2CP

So %age = {(100 - 80)/1.2}/80/1.2

= 40/80 = 50%

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Manager
Joined: 04 Aug 2011
Posts: 52
Followers: 0

Kudos [?]: 2 [0], given: 0

A difficult math (1) [#permalink]  13 Aug 2011, 05:08
A merchant sells an item at a 20% dicount, but still makes a gross profit of 20% of the cost. What percent of the cost would the gross profit on the item heve been if it had been sold without the discount?

a) 20%
b) 40%
c) 50%
d) 60%
e) 75%
A difficult math (1)   [#permalink] 13 Aug 2011, 05:08
Similar topics Replies Last post
Similar
Topics:
A merchant sells an item at a 20 percent discount, but still 5 28 Jul 2005, 05:04
Armani sells a pair of jeans at a 20% discount, but still 2 10 Dec 2005, 19:49
A merchant sells an item at a 20% discount, but still makes 1 21 Oct 2007, 12:59
1 Merchant Makes A Profit of 20% on Selling Price 3 10 Jul 2010, 20:28
A merchant sells an item at a 20% discount, but still makes 13 13 Sep 2007, 22:57
Display posts from previous: Sort by