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# A chair store sold a certain chair to a collector for 40%more than the

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Manager
Joined: 06 May 2019
Posts: 104
Location: India
Schools: LBS '22
GMAT 1: 710 Q51 V35
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WE: Information Technology (Computer Software)
A chair store sold a certain chair to a collector for 40%more than the  [#permalink]

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Updated on: 03 Dec 2019, 22:53
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Difficulty:

45% (medium)

Question Stats:

70% (02:54) correct 30% (03:21) wrong based on 23 sessions

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A chair store sold a certain chair to a collector for 40%more than the store had originally paid for the chair. When the collector tried to resell the chair to the store, the store bought it back at 60%of what the collector had paid. The shop then sold the chair again at a profit of 75%on its buyback price. If the difference between the chair's original cost to the shop and the amount the collector got from reselling it back to the shop is $176, for how much did the shop sell the chair the second time? A.$1,243
B. $1,439 C.$1,617
D. $1,851 E.$2,025

Originally posted by JiddiHuMain on 03 Dec 2019, 21:08.
Last edited by Bunuel on 03 Dec 2019, 22:53, edited 2 times in total.
Edited the question.
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Joined: 01 May 2017
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Location: India
Re: A chair store sold a certain chair to a collector for 40%more than the  [#permalink]

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03 Dec 2019, 21:48
A chair store sold a certain chair to a collector for 40%more than the store had originally paid for the chair. When the collector tried to resell the chair to the store, the store bought it back at 60%of what the collector had paid. The shop then sold the chair again at a profit of 75%on its buyback price. If the difference between the chair's original cost to the shop and the amount the collector got from reselling it back to the shop is $176, for how much did the shop sell the chair the second time?$1,243
$1,439$1,617
$1,851$2,025

Let the Cost price = x
First SP = 1.4*x
return price = 1.4*0.6*x

CP - Return Price = 176
x - 1.4*0.6*x = 176
0.16*x = 176
x = 176/0.16
x = 1100

Second SP = 1.75*(return price)
=1.75*1.4*0.6*x
= 1617

Correct Option is C
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Posts: 8327
Re: A chair store sold a certain chair to a collector for 40%more than the  [#permalink]

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03 Dec 2019, 21:54
JiddiHuMain wrote:
A chair store sold a certain chair to a collector for 40%more than the store had originally paid for the chair. When the collector tried to resell the chair to the store, the store bought it back at 60%of what the collector had paid. The shop then sold the chair again at a profit of 75%on its buyback price. If the difference between the chair's original cost to the shop and the amount the collector got from reselling it back to the shop is $176, for how much did the shop sell the chair the second time?$1,243
$1,439$1,617
$1,851$2,025

Let the initial price be x.
The cost to collector is 1.4x and the selling price of collector back to store =1.4*0.6=0.84x
Now it is given that x-0.84x=176....x=176/0.16=1100

So the store buys it back for 1100*0.84=924
Now this is sold at 75% profit = 924*1.75=924*175/100=924*7/4=231*7=1617

C

Other way to avoid decimals is to take x as 100.
So sold to collector at 140, then taken back at 140*60/100=84
Difference =100-84=16.
So if initial was 100, the difference is 16, so difference of 176 will be when the cost is 100*176/16=1100.
So final cost =1100*0.84=924 and a profit of 75% means 924*175/100=1617
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Joined: 03 Nov 2019
Posts: 54
Re: A chair store sold a certain chair to a collector for 40%more than the  [#permalink]

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03 Dec 2019, 21:59
Let initial price of the Store: 100 unit
Cost to Collector= 140
Buyback Price to store= 60% of 140= 84
Second time selling Price of Store= 75 % profit on 84=147

Now 100- 84 = 16 units = 176
Therefore: 147 unites= 176*147/16 = 11*147= 1617.

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Joined: 12 Apr 2019
Posts: 365
Re: A chair store sold a certain chair to a collector for 40%more than the  [#permalink]

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04 Dec 2019, 03:17
This is a question on the concept of successive percentage changes. I’d use the fractional equivalent of percentages extensively in this question to make the calculations simpler and faster.

Let the chair’s original cost to the shop be $x. On selling it to the collector at 40% profit, they obtained$$$\frac{7x}{5}$$.

When the collector sold it back to them, they bought it at 60% of what he had paid. Therefore, the price at which they bought it back = $$\frac{3}{5} * \frac{7x }{ 5} =  \frac{21x }{25}$$.

The difference between the shop’s original cost and the money that it paid (or the money that the collector got back) = x – $$\frac{21x}{25}$$ = $$$\frac{4x}{25}$$. The question says that this is equal to$176. Equating and solving for x, we get x = 1100.

Therefore, selling price of the shop when it sold the chair again = $$\frac{7}{4} * \frac{21x }{ 25} = \frac{147x}{100}$$ = \$ 1617.

The correct answer option is C.

In questions like these on percentages, the more methodical you are in analyzing statements stage by stage, the better your accuracy will be. Observe how we solved the question in small stages, evaluating the answer of each stage and using that as the input for the next stage.

Hope that helps!
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Re: A chair store sold a certain chair to a collector for 40%more than the   [#permalink] 04 Dec 2019, 03:17
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