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

It is currently 31 Jul 2015, 03:48
GMAT Club Tests

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
VP
VP
User avatar
Joined: 08 Jun 2005
Posts: 1146
Followers: 6

Kudos [?]: 136 [0], given: 0

A merchant sells an item at a 20% discount, but still makes [#permalink] New post 13 Sep 2007, 22:57
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (02:22) correct 38% (01:23) wrong based on 130 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%
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Jun 2014, 01:47, edited 1 time in total.
Edited the question and added the OA.
1 KUDOS received
Intern
Intern
avatar
Joined: 14 Mar 2005
Posts: 28
Followers: 0

Kudos [?]: 5 [1] , given: 0

 [#permalink] New post 13 Sep 2007, 23:46
1
This post received
KUDOS
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
Director
avatar
Joined: 17 Sep 2005
Posts: 927
Followers: 3

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

 [#permalink] New post 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
Director
User avatar
Joined: 08 Jun 2007
Posts: 584
Followers: 2

Kudos [?]: 80 [0], given: 0

Re: Merchant Sells Item Discount [#permalink] New post 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
Manager
avatar
Joined: 29 Aug 2007
Posts: 110
Followers: 1

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

 [#permalink] New post 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
VP
User avatar
Joined: 08 Jun 2005
Posts: 1146
Followers: 6

Kudos [?]: 136 [0], given: 0

 [#permalink] New post 14 Sep 2007, 13:34
1
This post was
BOOKMARKED
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
Director
User avatar
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait
Followers: 13

Kudos [?]: 181 [0], given: 0

 [#permalink] New post 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%]
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2028
Followers: 140

Kudos [?]: 1181 [0], given: 376

Re: Merchant Sells Item Discount [#permalink] New post 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

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 21 Sep 2010
Posts: 17
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Merchant Sells Item Discount [#permalink] New post 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
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5746
Location: Pune, India
Followers: 1445

Kudos [?]: 7587 [2] , given: 186

Re: Merchant Sells Item Discount [#permalink] New post 06 Jan 2011, 21:45
2
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
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
Ques.jpg [ 13.44 KiB | Viewed 13889 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

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 760
Followers: 14

Kudos [?]: 74 [0], given: 42

Re: Merchant Sells Item Discount [#permalink] New post 12 Mar 2011, 07:31
Answer is C.

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
SVP
avatar
Joined: 16 Nov 2010
Posts: 1678
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 364 [0], given: 36

Premium Member Reviews Badge
Re: Merchant Sells Item Discount [#permalink] New post 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%

Answer is C.
_________________

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

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5697
Followers: 322

Kudos [?]: 62 [0], given: 0

Premium Member
Re: A merchant sells an item at a 20% discount, but still makes [#permalink] New post 06 Jun 2014, 01:37
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 23

Kudos [?]: 1010 [0], given: 193

Re: A merchant sells an item at a 20% discount, but still makes [#permalink] New post 06 Jun 2014, 02:15
Let the selling price = 300

Discount = 20% = 60

Received Amount from customer = 240

240 includes 20% profit

Cost price \(= 240 * \frac{120}{100} = 200\)

If no discount given, then shopkeeper would have earned 300 - 200 = 100 on the item costing 200

His "would be" profit percentage \(= \frac{100}{200} * 100 = 50%\)

Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
Joined: 10 Mar 2014
Posts: 180
Followers: 1

Kudos [?]: 22 [0], given: 12

Premium Member CAT Tests
Re: A merchant sells an item at a 20% discount, but still makes [#permalink] New post 06 Jun 2014, 05:40
Here we can say selling price = s and purchase price or cost is p

it is given in question

.8s = 1.2p

s/p = 1.2/8 = 1.5

say p = 20 , s= 30 we can take any number in this combination.

now 20% discount on 30 i.e. sp is 24 and this is 20% profit on purchase price.

if without discount we sell then 30 is 150 %of 20 so its 50% more then purchase price.

Hope it helps.
Re: A merchant sells an item at a 20% discount, but still makes   [#permalink] 06 Jun 2014, 05:40
    Similar topics Author Replies Last post
Similar
Topics:
1 A milk vendor sells milk at Cost Price but still gains 20%. chris93 1 28 Oct 2012, 20:48
A toy store regularly sells all stock at a discount of 20% Jasontuyj2012 2 07 Aug 2011, 04:08
26 Experts publish their posts in the topic A dealer offers a cash discount of 20% and still makes a pro feruz77 12 25 Nov 2010, 07:20
1 Experts publish their posts in the topic A toy store regularly sells all stock at a discount of 20 pzazz12 15 25 Oct 2010, 04:40
1 Merchant Makes A Profit of 20% on Selling Price farukhawais 3 10 Jul 2010, 20:28
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.