A shop purchased a pair of sunglasses for $120

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conquistador: Master | Next Rank: 500 Posts; Posts: 266; Joined: Fri Sep 19, 2014 4:00 am; Thanked: 4 times; Followed by:1 members

A shop purchased a pair of sunglasses for $120

by conquistador » Sun Oct 11, 2015 7:41 am

Source:Gmatclub

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

OA is E

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Source: Beat The GMAT — Problem Solving | Sun Oct 11, 2015 7:41 am

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pm; Thanked: 115 times; Followed by:3 members

by theCEO » Sun Oct 11, 2015 8:38 am

Mechmeera wrote:Source:Gmatclub

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

OA is E

Purchase price = 120
Original selling price = 120+x = y; x=0.25y
Original selling price = 120+0.25y = y; y-0.25y = 120; y=160
Original selling price = 160

New Selling price = 160x0.8 = 128

Profit = 128-120 = 8

ans = e

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by [email protected] » Sun Oct 11, 2015 9:32 am

Hi Mechmeera,

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: E

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Rich

Contact Rich at [email protected]

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by GMATGuruNY » Sun Oct 11, 2015 2:35 pm

Mechmeera wrote: 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 x = the non-discounted selling price.

Since the MARKUP is equal to 25% of the non-discounted selling price, the PURCHASE PRICE of $120 is equal to 75% of the non-discounted selling price:
120 = (3/4)x
480 = 3x
x = 160.

Discounted selling price = 160 - 20% of 160 = 160-32 = 128.
Profit = (discounted selling price) - (purchase price) = 128-120 = $8.

The correct answer is E.

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by Scott@TargetTestPrep » Thu Feb 15, 2018 10:20 am

conquistador wrote:Source:Gmatclub

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

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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