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A clock store sold a certain clock to a collector for 20 per

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A clock store sold a certain clock to a collector for 20 per [#permalink] New post 11 Jun 2007, 20:02
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A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time?

A. $270
B. $250
C. $240
D. $220
E. $200
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 May 2014, 08:27, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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 [#permalink] New post 11 Jun 2007, 20:42
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$270

Original Price = x
Sold to collector at 1.2x

re-buy price = 1.2x * 0.5 = 0.6x

therefore, x - 0.6x = 100; x = 250

second selling price = 1.8 * 0.6 * 250 = 270

Hope, this is not too confusing :)
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 [#permalink] New post 12 Jun 2007, 09:52
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100 % - original price
120 % - sell 1
60 % - bought 2
180*60/100 = 108 % - sell 2

100$ - 40%
x - 108 %
x= 100*108/40 = 270

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Re: clock sale - ps [#permalink] New post 06 May 2014, 08:11
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Re: A clock store sold a certain clock to a collector for 20 per [#permalink] New post 06 May 2014, 19:22
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hsk wrote:
A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time?

A. $270
B. $250
C. $240
D. $220
E. $200


Assume numbers and then use ratios to fit them in with the actual numbers.

Say the store bought the clock for $100 and sold it to the collector for $120. The store bought back from the collector for $60 and sold it back at $60*18/10 = $108
Here, difference between original cost ($100) and buy back price ($60) is $40. But actually it is given to be $100 which is 2.5 times 40. So the shop sold the clock a second time for $108*2.5 = $270
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Re: A clock store sold a certain clock to a collector for 20 per [#permalink] New post 01 Jun 2015, 22:35
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Re: A clock store sold a certain clock to a collector for 20 per [#permalink] New post 01 Jun 2015, 23:44
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The question is a bit wordy and gives us a series of percentages on which we need to work on. Going step wise is the key to not miss out on any of the information. Presenting the detailed step wise solution

Step-I- Store buys the clock
Let's assume the original price of clock paid by the store to be \(x\)

Step-II- Collectors buys the clock from the store
Extra amount paid by collector to buy the clock = \(20\)% of \(x\)

Therefore price at which collector buys the clock = \(x + 20\)% of \(x = 1.2x\)

Step-III- Store buys back the clock from collector
Price at which the store buys the clock = \(50\)% of price collector paid \(= 50\)% of \(1.2x = 0.6x\)

Step-IV- Store resells the clock
Price at which store resells the clock = \(0.6x + 80\)% of \(0.6x = 0.6x * 1.8\)

Now, we are given that difference between clock's original price and clock's buy back price = \(100\)

\(x - 0.6x = 100\) i.e. \(x = 250\)

We are asked to find the price at which the store resells the clock = \(0.6x * 1.8 = 0.6 * 250 * 1.8 = 270\)

Hope this helps :)

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Re: A clock store sold a certain clock to a collector for 20 per   [#permalink] 01 Jun 2015, 23:44
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