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A shop purchased a pair of sunglasses for $120 and was

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A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 02 Oct 2012, 14:54
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M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 02 Oct 2012, 15:16
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2
Ans is E

Sale Price(SP) = 120 + Markup(MP)
--> Mp = SP-120
and given MP=SP/4 ( 25% is 1/4th)

so SP/4= SP-120
3SP/4= 120
SP=160

Now a discount of 20% is given so NEW SP is .8 *160 =128

Profit=128-120 =8$
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 02 Oct 2012, 18:55
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3
smartass666 wrote:
M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8


A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?

A. $0
B. $2
C. $4
D. $6
E. $8

Let the markup be \($x\), so \(x\) must be 25% of the selling price, which would be \(120+x\): \(x=0.25(120+x)\) --> \(x=40\). Hence the selling price was \(120+40=160\).

The price after the discount of 20% would be \(160*0.8=128\) --> gross profit on the sale: final selling price - cost of the sunglasses = \($128 - $120 = $8\).

Answer: E.
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 02 Oct 2012, 22:53
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Markup=sp-cp ..

markup=.25SP

so..

.25sp=sp-120

.75sp=120
selling price will be 160

160*.80=128.. multiplied by .80 because we price dec by 20 %..

so ..gross profit=sp-cp..128-120=8..
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 03 Oct 2012, 12:04
smartass666 wrote:
M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8



Gud question..need to keep eyes wide open... :shock: :shock:

Answer: - E :-D :-D
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Jun 2013, 23:11
Bunuel wrote:
smartass666 wrote:
M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8


A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?

A. $0
B. $2
C. $4
D. $6
E. $8

Let the markup be \($x\), so \(x\) must be 25% of the selling price, which would be \(120+x\): \(x=0.25(120+x)\) --> \(x=40\). Hence the selling price was \(120+40=160\).

The price after the discount of 20% would be \(160*0.8=128\) --> gross profit on the sale: final selling price - cost of the sunglasses = \($128 - $120 = $8\).

Answer: E.


I am confused a little bit!

Because for me these two wordings have different meaning:
a) sale at margin of 25% => I will earn 25 above my cost or my purchase price will be 75% of the sale price => hence sale price 160
b) sale at purchase price plus mark up of 25% => I will earn 25% on top purchase price or purchase price *(1+25%) => hence sale price 150

Please suggest how should I approach such problems?
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Jun 2013, 23:15
samatace wrote:
Bunuel wrote:
smartass666 wrote:
M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8


A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?

A. $0
B. $2
C. $4
D. $6
E. $8

Let the markup be \($x\), so \(x\) must be 25% of the selling price, which would be \(120+x\): \(x=0.25(120+x)\) --> \(x=40\). Hence the selling price was \(120+40=160\).

The price after the discount of 20% would be \(160*0.8=128\) --> gross profit on the sale: final selling price - cost of the sunglasses = \($128 - $120 = $8\).

Answer: E.


I am confused a little bit!

Because for me these two wordings have different meaning:
a) sale at margin of 25% => I will earn 25 above my cost or my purchase price will be 75% of the sale price => hence sale price 160
b) sale at purchase price plus mark up of 25% => I will earn 25% on top purchase price or purchase price *(1+25%) => hence sale price 150

Please suggest how should I approach such problems?


We are not told that markup was 25%, we are told that the markup amount was 25% of the selling price.
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Jun 2013, 23:44
Thanks. I missed that part. Now it makes sense
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 16 Aug 2015, 15:44
The thing that still really confuses me about this question is when it mentions "...and was selling it at a price that equaled the purchase price of the sunglasses plus a markup ..."

I understand a few vocabulary terms. The "Cost Price" is the price at which a shop owner, business, whomever pays for a single widget. The "Selling Price" is the price that a customer pays for the the widget. I thought that "Purchase Price" was another term that was used in the same manner of "Selling Price", so in this question that is why I was confused. Why would the term Purchase Price be used to represent the price at which the shop paid for the sunglasses?

If you search this website for the term "The purchase price of Beth's new car, including the sales" you will find a topic / question that uses the term "Purchase Price" differently (can't post links because I'm a new member).
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 16 Aug 2015, 16:05
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jimmygm23 wrote:
The thing that still really confuses me about this question is when it mentions "...and was selling it at a price that equaled the purchase price of the sunglasses plus a markup ..."

I understand a few vocabulary terms. The "Cost Price" is the price at which a shop owner, business, whomever pays for a single widget. The "Selling Price" is the price that a customer pays for the the widget. I thought that "Purchase Price" was another term that was used in the same manner of "Selling Price", so in this question that is why I was confused. Why would the term Purchase Price be used to represent the price at which the shop paid for the sunglasses?

If you search this website for the term "The purchase price of Beth's new car, including the sales" you will find a topic / question that uses the term "Purchase Price" differently (can't post links because I'm a new member).


The wording and definition of "purchase price" is still the same (even for the example you are quoting!). Purchase price in the example of pair of sunglasses, is the cost price for the shop, ie the price that the shopkeeper would have paid for the pair of sunglasses.

Purchase price in the example quoted by you is also the same "effect". The purchase price in this case is what Beth would have paid for the car.
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 16 Aug 2015, 16:08
Thank you Engr2012! I guess the conclusion is that the term "Purchase Price" is a more flexible term unlike "Cost Price" and "Selling Price" that can be applied to different aspects of a transaction.
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Nov 2015, 05:48
I'm sorry if this is an incredibly dumb question but how are we getting that x=40? I get x = .25(120+x), but that becomes 30+x does it not? When I multiply 120 by .25 it's 30 not 40, what am I missing here?
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Nov 2015, 06:37
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redfield wrote:
I'm sorry if this is an incredibly dumb question but how are we getting that x=40? I get x = .25(120+x), but that becomes 30+x does it not? When I multiply 120 by .25 it's 30 not 40, what am I missing here?


There is no such thing as a dumb question.

The benefit of a linear equation or any equation for that matter is that you can check whether the value you calculated is correct.

You are given,

x=.25(120+x) ---> check for x=30, RHS becomes = .25(120+30) = .25(150) = 37.5 \(\neq\)30 (=LHS). Thus x = 30 is not the correct answer.

Coming back to the original equation,

x=.25(120+x) (if you are afraid of making a mistake with decimals, realise that .25 = 1/4 ) ---> x = (1/4)*(120+x) --> 4x = 120+x ---> 3x=120 --> x=40

With decimals, x=.25(120+x) ---> x=.25*120+.25x ---> .75x=30 ---> x = 30/.75 = 40 (.75=3/4).

Hope this helps.
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Nov 2015, 06:43
Engr2012 wrote:
With decimals, x=.25(120+x) ---> x=.25*120+.25x ---> .75x=30 ---> x = 30/.75 = 40 (.75=3/4).

Hope this helps.


I totally missed on the distribution aspect of it, I'm embarrassed by myself! Thank you for breaking it out like that, definitely helped.
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Nov 2015, 08:05
smartass666 wrote:
M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8


Given: Cost price = $120
Assume the markup to be x

Hence the Original Selling Price = 120 + x
But, we know that x = 0.25*(120 + x)
Hence x = 40

Therefore the Original Selling price = $160

Now, the shopkeeper decides to give a discount on this.
Final Selling Price = 0.8*160 = 128

Hence the Gross Profit = 128 - 120 = $8
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A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 26 Nov 2015, 10:27
smartass666 wrote:
M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8


All the methods posted here are unique , I would like to share my approach

I constructed a 2/2 grid as shown below.


Profit after decrease in SP by 20% and subsequent gross profit by selling an item for $ 120 is - (5 / 75 )*120 => $8

Hence answer is (E) $8
Attachments

Markup.PNG
Markup.PNG [ 2.81 KiB | Viewed 5277 times ]


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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 29 Dec 2015, 10:43
i got this exact question on my exam on Dec 21!!! this is a GMAC question
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 13 Feb 2018, 21:12
Hi All,

The math involved in this question is essentially just arithmetic, but you'll have to be careful with how you organize your work (and adding some extra 'labeling' will probably help).

We're told that the original cost of a pair of sunglasses was $120 and the planned selling price included a mark-up equal to 25% of the SELLING PRICE.

Original Cost = $120
Planned Sell Price = $120 + (25%)(Sell Price) = Sell Price

120 + .25P = P
120 = .75P
120 = (3/4)P
(4/3)(120) = P
160 = P

Now we know the planned sell price was $160.

Next, we're told that the shop owner decreased THIS price by 20%....

$160 - (20%)($160) = $160 - $32 = $128

With the original cost ($120) and this new sell price ($128), the gross profit was 128 - 120 = $8

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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 15 Feb 2018, 10:07
smartass666 wrote:
M07-Q33
A shop purchased a pair of sunglasses for $120 and was selling it at a price that equaled the purchase price of the sunglasses plus a markup that was 25 percent of the selling price. After some time a shop owner decided to decrease the selling price by 20 percent. What was the shop's gross profit on this sale?
$0
$2
$4
$6
$8


If we let the selling price = r, the selling price for the glasses is:

r = 120 + 0.25r

0.75r = 120

r = 160

With the 20% decrease in price the new selling price is 0.8 x 160 = 128.

The profit on the sale is 128 - 120 = 8 dollars

Answer: E
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Re: A shop purchased a pair of sunglasses for $120 and was  [#permalink]

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New post 06 Jul 2018, 07:26
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How is the above question different from this:

A shoe shop owner lists the price of a pair of shoes as the price at which he purchased the pair from the manufacturer plus a markup which is equal to 40 percent of the selling price. After some time, he offers a discount on the shoes which is equal to 20 percent of the selling price. Which of the following best represents the profit, as a percentage of the purchase price, which he earns on selling the pair of shoes?


A. 11%
B. 12%
C. 17%
D. 20%
E. 25%

Yet the OA for this question is E. Please suggest- why the equations used here differ from this question
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Re: A shop purchased a pair of sunglasses for $120 and was &nbs [#permalink] 06 Jul 2018, 07:26

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