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

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A merchant sells an item at a 20% discount, but still makes [#permalink] New post 13 Sep 2007, 22:57
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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. 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.
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 [#permalink] New post 13 Sep 2007, 23:46
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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)
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 [#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.

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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%
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 [#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?
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 [#permalink] New post 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

:)
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 [#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%]
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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%.
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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
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Re: Merchant Sells Item Discount [#permalink] New post 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
Ques.jpg [ 13.44 KiB | Viewed 11639 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: 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%
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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.
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Re: A merchant sells an item at a 20% discount, but still makes [#permalink] New post 06 Jun 2014, 01:37
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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
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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
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