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A shop purchased a pair of sunglasses for $120 and was Updated on: 11 Aug 2025, 04:06
Originally posted by Bunuel on 02 Oct 2012, 15:54.
Last edited by Bunuel on 11 Aug 2025, 04:06, edited 1 time in total.
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A shop bought a pair of sunglasses for $120 and was selling them at a profit which was equal to 25% of the selling price. Later, the shop owner decided to reduce the selling price by 20%. What was the shop's gross profit on the sale?

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


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Bunuel
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A shop purchased a pair of sunglasses for $120 and was 02 Oct 2012, 19:55
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Official Solution:

A shop bought a pair of sunglasses for $120 and was selling them at a profit which was equal to 25% of the selling price. Later, the shop owner decided to reduce the selling price by 20%. What was the shop's gross profit on the sale?

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


Cost price + Profit = Selling price;

Cost price + 0.25*Selling price = Selling price;

120 + 0.25*Selling price = Selling price;

0.75*Selling price = 120;

Selling price = $160

After the price reduction, the New Selling price would be 0.8*160 = $128. Therefore, the profit would be New Selling price - Cost price = 128 - 120 = $8.


Answer: E
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A shop purchased a pair of sunglasses for $120 and was 02 Oct 2012, 16:16
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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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A shop purchased a pair of sunglasses for $120 and was 02 Oct 2012, 23:53
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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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A shop purchased a pair of sunglasses for $120 and was 27 Jun 2013, 00:11
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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

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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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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A shop purchased a pair of sunglasses for $120 and was 27 Jun 2013, 00:15
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Bunuel
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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

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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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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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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jimmygm23
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).
Show more

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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A shop purchased a pair of sunglasses for $120 and was 26 Nov 2015, 06:48
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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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redfield
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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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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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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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
Option E
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A shop purchased a pair of sunglasses for $120 and was 26 Nov 2015, 11:27
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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
Show more

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 21335 times ]

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A shop purchased a pair of sunglasses for $120 and was 13 Feb 2018, 22:12
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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

Final Answer:
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E

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A shop purchased a pair of sunglasses for $120 and was 15 Feb 2018, 11:07
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smartass666
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
Show more

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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A shop purchased a pair of sunglasses for $120 and was 07 Jul 2018, 03:34
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smartass666
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
Show more

Since the markup is equal to \(\frac{1}{4}\) of the original selling price, and the original selling price is discounted by \(\frac{1}{5}\), the original selling price must be a multiple of 4 and 5 -- in other words, a MULTIPLE OF 20 -- that is greater than the $120 purchase price:
140, 160, 180...

The answer choices indicate that the discounted selling price yields a profit between $0 and $8, inclusive.
Implication:
Reducing one of the values above by \(\frac{1}{5}\) must yield a discounted selling price between $120 and $128, inclusive.

Only the green option is viable:
\(160 - \frac{1}{5}*160 = 160 - 32 = 128.\)
Since the discounted selling price = 128, the profit = 128-120 = 8.

Show Spoiler
E
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