GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Aug 2018, 00:26

### 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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

VP
Joined: 08 Jun 2005
Posts: 1139
A merchant sells an item at a 20% discount, but still makes  [#permalink]

### Show Tags

Updated on: 06 Jun 2014, 02:47
21
00:00

Difficulty:

55% (hard)

Question Stats:

71% (01:32) correct 29% (01:42) wrong based on 460 sessions

### HideShow timer Statistics

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%

Originally posted by KillerSquirrel on 13 Sep 2007, 23:57.
Last edited by Bunuel on 06 Jun 2014, 02:47, edited 1 time in total.
Edited the question and added the OA.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8188
Location: Pune, India
Re: Merchant Sells Item Discount  [#permalink]

### Show Tags

06 Jan 2011, 22:45
6
11
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 88238 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

Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! ##### Most Helpful Community Reply Intern Joined: 14 Mar 2005 Posts: 28 ### Show Tags 14 Sep 2007, 00:46 3 3 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)
##### General Discussion
Director
Joined: 17 Sep 2005
Posts: 873

### Show Tags

14 Sep 2007, 09:18
1
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: 560
Re: Merchant Sells Item Discount  [#permalink]

### Show Tags

14 Sep 2007, 09:29
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: 110

### Show Tags

14 Sep 2007, 14:13
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: 1139

### Show Tags

14 Sep 2007, 14:34
1
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: 579
Location: Kuwait

### Show Tags

14 Sep 2007, 15:03
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%]
Retired Moderator
Joined: 20 Dec 2010
Posts: 1879
Re: Merchant Sells Item Discount  [#permalink]

### Show Tags

05 Jan 2011, 06:48
1
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%.
_________________
Intern
Joined: 21 Sep 2010
Posts: 16
Re: Merchant Sells Item Discount  [#permalink]

### Show Tags

05 Jan 2011, 12:43
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%

Director
Joined: 01 Feb 2011
Posts: 671
Re: Merchant Sells Item Discount  [#permalink]

### Show Tags

12 Mar 2011, 08:31

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%
Retired Moderator
Joined: 16 Nov 2010
Posts: 1460
Location: United States (IN)
Concentration: Strategy, Technology
Re: Merchant Sells Item Discount  [#permalink]

### Show Tags

12 Mar 2011, 09:46
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)

GMAT Club Premium Membership - big benefits and savings

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A merchant sells an item at a 20% discount, but still makes  [#permalink]

### Show Tags

06 Jun 2014, 03:15
1
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 $$= \frac{100}{200} * 100 = 50%$$

_________________

Kindly press "+1 Kudos" to appreciate

Manager
Joined: 10 Mar 2014
Posts: 212
Re: A merchant sells an item at a 20% discount, but still makes  [#permalink]

### Show Tags

06 Jun 2014, 06:40
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.
Manager
Joined: 23 Sep 2015
Posts: 87
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38
GMAT 2: 690 Q47 V38
GPA: 3.5
Re: A merchant sells an item at a 20% discount, but still makes  [#permalink]

### Show Tags

04 Nov 2015, 13:19
I did it a bit differently

I first picked a cost = 60

Therefore - GP = 20%cost = 12

Cost + GP = Sale Price = 72

Sale price of 72 represents 80% of Initial cost of the item --> 72/80% = 90

From here i took the 90 as the main Sale price, subtracted cost (60) and got new GP of 30

SP - 90
C - (60)
____
GP - 30

30/60 = 50%
Intern
Joined: 28 Feb 2017
Posts: 4
Re: A merchant sells an item at a 20% discount, but still makes  [#permalink]

### Show Tags

29 Jan 2018, 08:14
Honestly its very easy question provided you pick the right numbers

Lets assume the SP is 120. So offering a 20% discount, the merchant sells at 96 and on this he make a 20% profit. So his cost is 80.

Now of if he sells without the discount then the profit on cost would be 120-80/80 = 50%..

Should be able to do it under 1 min though
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12185
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A merchant sells an item at a 20% discount, but still makes  [#permalink]

### Show Tags

28 Feb 2018, 22:18
Hi All,

This question is perfect for TESTing VALUES, but you have to be very careful about how you do the math. Let's break this into pieces...

A merchant sells an item at a discount and makes a gross profit of 20% on the cost.

Let's TEST VALUES:
Cost = $100 Discount Price =$120
Here we have a 20% profit on the cost...

Regular Price = $X Now, let's factor in the fact that the sale price was a 20% discount...$120 = X - (.2)(X)
$120 = .8X$1200 = 8X
$150 = X So, the regular price was$150.

We're asked what the profit would have been WITHOUT the discount:
Cost: $100 Regular Price =$150

Profit = (150 - 100)/100 = 50/100 = 50%

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 28 May 2017
Posts: 26
Location: India
Concentration: Finance, Marketing
GPA: 3.87
WE: Web Development (Mutual Funds and Brokerage)
Re: A merchant sells an item at a 20% discount, but still makes  [#permalink]

### Show Tags

19 Jun 2018, 12:59
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%

I am going to tell you an amazing way to do this in matter of 10 seconds. Please have patience with me and see below. Once you grab the concept profit loss and mixtures questions will become your strongest points.

120/100 = 80/100 * x

if you do basic calculations X is 3/2
This means 50% increase. This is the answer

how I did it? See when we say he gave a discount of 20% , it is upon some value be it 100 or 50 or 25 or 78 or 10000 --- > so 20% discount means he sold at 80% of the value? got it? see how.

100-20 / 100 = 0.8,
50-10/50 = 0.8

take any value the ratio will be 8/10
now we can see he clearly made a loss but must have done something that resulted in 20% overall profit. Right? That something is x in the equation.

so that X is your answer when he doesn't give the discount.

In short, no need to take values as left hand common part will be cancelled with right side of equation.

Good Luck
Re: A merchant sells an item at a 20% discount, but still makes &nbs [#permalink] 19 Jun 2018, 12:59
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.