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Difficult Math Problem #59 - Percentage

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Difficult Math Problem #59 - Percentage

by 800guy » Sun Nov 19, 2006 2:59 pm
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%

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Re: Difficult Math Problem #59 - Percentage

by gmat_enthus » Mon Nov 20, 2006 6:44 am
800guy 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%

Let the marked price be x.
SP = 0.8x

SP-CP=.2CP => SP=.2CP => CP=0.8x/1.2

If sold without discount profit = (x - 0.8/1.2x)/(0.8/1.2x) = 50%

Ans C
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OA

by 800guy » Wed Nov 22, 2006 6:09 pm
OA:

Lets suppose original price is 100.

And if it sold at 20% discount then the price would be 80

but this 80 is 120% of the actual original price...so 66.67 is the actual price of the item

now if it sold for 100 when it actually cost 66.67 then the gross profit would be 49.99% i.e. approx 50%
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by dieterdubois » Tue Sep 08, 2009 10:58 am
Following the logic of the other replies, and reading the question carefully, I would assume that the solution needs to be the following:

49,99%/66.67% = 75%
It is the gross profit on the item of the cost not of the the profit on the sales price. Or am I completely misreading the question?
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by bharathh » Tue Sep 08, 2009 11:10 am
Let msrp or asking price be X

Selling price is 80% of X = 4/5 of X
However selling price is 120% of original price

6/5 of O

4X/5 = 6O/5

4X = 6O
X/O = 6/4 = 1.5

Therefore msrp or original asking price is 50% more
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Different approach

by navdeepbajwa » Wed Oct 21, 2009 2:07 am
I solved this problem by assuming Cost Price instead of Markedup price

Let the CP be 100

Since he makes a profit of 20% so SP=120

Let X be the marked up price since the item is sold at a discount of 20% of Mark up price so

0.8X=120
X=150

So percent of cost would be 150-100/100 *100=50%
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by Callum29D » Tue Jan 10, 2012 9:02 am
Ok here is my solution:
Let the sell price (sp) without the discount be X. Let the cost be Y. Then the gross profit (GP) is GP = 4X/5 - Y. (this is the price we sold it for minus the cost to the merchant). We know that this is equal to 20% of the cost. Therefore: 4X/5 - Y = Y/5.
This will give us a value for X in terms of Y: X = (6Y/5)(5/4) = 6Y/4 = 3Y/2.


If the item was sold without discount, then GP = X-Y. Substitute X=3Y/2 into this equation to get:
GP = 3Y/2 - Y = Y/2.

So GP = Y/2 which is precisely the same as 50% of Y. So without the discount, the item would make a gross profit of 50% of the cost Y.
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by Abhishek009 » Tue Jan 10, 2012 9:11 am
800guy 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%

Let the marked price be 100

Selling price after the discount is 80

Now this 80 represents CP + Profit...

Let CP b 100 , Sp is 120

Now 120 represents 80

1 Represents 120/80

So 100 represents (120/80)*100 =>150

So , Cp is 100 and Sp is 150 , there is a profit of 50%...
Abhishek
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by GMATGuruNY » Tue Jan 10, 2012 10:03 am
800guy 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%

An alternate approach: plug in the answers, which represent the profit without the discount.
Let the cost = 100.

Answer choice C: profit = 50%.
Selling price = 100 + .5(100) = 150.
Discounted price = 150 - .2(150) = 120.
Profit with the discounted price = 120-100 = 20.
Profit/Cost = 20/100 = 20%.
Success!

The correct answer is C.
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by shayam » Tue Jan 10, 2012 10:51 am
For plug-in answer choice, how did you directly narrow down to 50% in this case?
I could have started with 40/60.. and this could have taken more time?
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by Callum29D » Tue Jan 10, 2012 11:16 am
I honestly don't think you should plug in the answers to see if you end up satisfying the initial conditions of the problem. If it was timed you have an 80% chance of getting it wrong the first time, a 75% chance of getting it wrong the second time, a 66.6666% chance of getting it wrong the third time and a 50% chance of getting it right the fourth time. All this trial and error wastes time.
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by GMATGuruNY » Tue Jan 10, 2012 11:57 am
shayam wrote:For plug-in answer choice, how did you directly narrow down to 50% in this case?
I could have started with 40/60.. and this could have taken more time?
The answer choices typically are given in increasing or decreasing order.
Here, the answer choices increase.
Start with C.
If C is too small, the correct answer must be D or E.
If C is too big, the correct answer must be A or B.
Try one of the remaining 2 answer choices.
If it works, select it; if not, select the other answer choice.
At most, you'll need to try 2 of the 5 answer choices.
In many cases, it will be necessary to try ONLY ONE answer choice.

Consider my solutions to the following problems:

https://www.beatthegmat.com/ratio-2-and- ... 01811.html.
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https://www.beatthegmat.com/tree-planted-t94510.html
https://www.beatthegmat.com/boat-t90471.html
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by GMATGuruNY » Tue Jan 10, 2012 12:13 pm
Callum29D wrote:I honestly don't think you should plug in the answers to see if you end up satisfying the initial conditions of the problem. If it was timed you have an 80% chance of getting it wrong the first time, a 75% chance of getting it wrong the second time, a 66.6666% chance of getting it wrong the third time and a 50% chance of getting it right the fourth time. All this trial and error wastes time.
At most you'll have to try 2 answer choices -- and in many cases -- only ONE answer choice.
Please see my second post.
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by ronnie1985 » Tue Jan 10, 2012 8:03 pm
50%
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by DonMiguel » Fri Feb 10, 2012 8:01 am
This is just a simple formula. very simple.

IF regular price = $100 & 20 × 258 ≈ 5.764×1018
discounted price = $100 - 20% = $80
c + .2c = 1.2c = 80 c = 66.6
profit is 100-66.66 = 33.33
33.33/66.66 = 50% (C)(1+m/100)*(1-d/100)=(1+p/100)
where m is mark up %, d is discount % and p is profit %.
SP = VC + GC = 20 × 258 ≈ 5.764×1018
If d = 20 and p = 20,
(1+m/100)*(1-20/100)=(1+20/100)
(1+m/100)*(4/5)=6/5)
Selling Price (Discounted Price) = 100%of MP - 20%MP
= 80% of MP. --------------->(1)
SP Discounted = 20% of CP ---->(2)
Profit = Selling Price - Original Cost Price
=> 20% of CP = 80% of MP - 100% CP
=> MP = 120CP/80 = 3/2 (CP)
If Item sold w/o Discount:
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
It means, 50% profit w/o discount!
so profit [100- 200/3] / [200/3 ] * 100 = 49.98%

THE ANSWER = 49.9837728287737365546377378888 !


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