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hsk
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A clock store sold a certain clock to a collector for 20 per Updated on: 06 May 2014, 09:27
Originally posted by hsk on 11 Jun 2007, 21:02.
Last edited by Bunuel on 06 May 2014, 09:27, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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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
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A
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A clock store sold a certain clock to a collector for 20 per 06 May 2014, 20:22
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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
Show more

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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A clock store sold a certain clock to a collector for 20 per 11 Jun 2007, 21:42
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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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A clock store sold a certain clock to a collector for 20 per 12 Jun 2007, 10:52
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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

A
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A clock store sold a certain clock to a collector for 20 per 02 Jun 2015, 00:44
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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 :)

Regards
Harsh
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A clock store sold a certain clock to a collector for 20 per 11 Jul 2015, 13:39
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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 :)

Regards
Harsh
Show more

Dear,

I have a basic question.

The author states: "The shop then sold the clock again at a profit of 80 percent on its buy-back price". Why is it suppose to multiply 0.6x*1.8? I think my confuse is related to the profit concept. For me, if I buy something at 100, and the cost of it is 80. I have a profit of 20/100 = 20%. Using the same logic on the question, if I buy something at 100 and I get a profit of 80%, the sales price must be 100/0.2. Thus, it is 500. Profit is 400/500=80%. It is a totally different aproach than to say 100*1,8.

Where my confuse is?

Kind regards...
Gonzalo
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A clock store sold a certain clock to a collector for 20 per 11 Jul 2015, 13:54
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gbascurs
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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 :)

Regards
Harsh

Dear,

I have a basic question.

The author states: "The shop then sold the clock again at a profit of 80 percent on its buy-back price". Why is it suppose to multiply 0.6x*1.8? I think my confuse is related to the profit concept. For me, if I buy something at 100, and the cost of it is 80. I have a profit of 20/100 = 20%. Using the same logic on the question, if I buy something at 100 and I get a profit of 80%, the sales price must be 100/0.2. Thus, it is 500. Profit is 400/500=80%. It is a totally different aproach than to say 100*1,8.

Where my confuse is?

Kind regards...
Gonzalo
Show more

Gonzalo, Profit is calculated = Selling price - Cost price. Profit % is always calculated on the cost price of the purchase and not on the selling price. You are calculating profit % on the selling price. This is where you are going wrong. I am assuming that in your example, you are buying something at 80 while you are selling it at 100, giving you an absolute profit of 20$ while your profit % will be 20/80 = 25% and not 20/100 = 20%.

Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 20% profit.
This means the clocks' selling price was C (1.2) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 50% the price at which the collector bought it.

Thus, you get = 1.2*0.5*C = 0.6 C

Furthermore, the store sells the clock for the second time for 80% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.8 = 1.8 * 0.6 C

Finally given that C - 0.6 C = 100 ----> C = 250$

Thus, the cost of the clock the second time around = 1.8*0.6 C = 1.8 * 0.6 * 250 = 270$. Hence A is the correct answer.
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A clock store sold a certain clock to a collector for 20 per 11 Jul 2015, 14:20
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gbascurs
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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 :)

Regards
Harsh

Dear,

I have a basic question.

The author states: "The shop then sold the clock again at a profit of 80 percent on its buy-back price". Why is it suppose to multiply 0.6x*1.8? I think my confuse is related to the profit concept. For me, if I buy something at 100, and the cost of it is 80. I have a profit of 20/100 = 20%. Using the same logic on the question, if I buy something at 100 and I get a profit of 80%, the sales price must be 100/0.2. Thus, it is 500. Profit is 400/500=80%. It is a totally different aproach than to say 100*1,8.

Where my confuse is?

Kind regards...
Gonzalo

Gonzalo, Profit is calculated = Selling price - Cost price. Profit % is always calculated on the cost price of the purchase and not on the selling price. You are calculating profit % on the selling price. This is where you are going wrong. I am assuming that in your example, you are buying something at 80 while you are selling it at 100, giving you an absolute profit of 20$ while your profit % will be 20/80 = 25% and not 20/100 = 20%.

Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 20% profit.
This means the clocks' selling price was C (1.2) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 50% the price at which the collector bought it.

Thus, you get = 1.2*0.5*C = 0.6 C

Furthermore, the store sells the clock for the second time for 80% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.8 = 1.8 * 0.6 C

Finally given that C - 0.6 C = 100 ----> C = 250$

Thus, the cost of the clock the second time around = 1.8*0.6 C = 1.8 * 0.6 * 250 = 270$. Hence A is the correct answer.
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Thank you a lot.

Here is the key of my misunderstanding: "Profit % is always calculated on the cost price of the purchase". I assumed it was on the sales price.
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A clock store sold a certain clock to a collector for 20 per 10 Nov 2015, 05:00
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x=starting price
therefore
x +20% = \(x +1/5x\) = \(6x/5\)
50% = 3x/5 BB Price
as per Q
x - \(3x/5\)=100
x=250
BB =150
80 %increment of 150 = 270
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A clock store sold a certain clock to a collector for 20 per 10 Nov 2015, 05:20
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hsk
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
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Let us assume the initial price (CP) of the clock to be 100x
We assume 100x to avoid the usage of decimals in case of x and avoid the usage of unitary method in case of 100

Transaction 1:
Store sold the clock to collector.
Selling Price = 20% more than CP = 120x

Transaction 2:
The collector sold it back to the store.
The new CP for the store = 60x (Store bought it back for 50% of the Selling Price)

Transaction 3:
Store sold it back at a profit of 80% on 60x = 108x

Now we are told that 100x - 60x = 100
This means x = 100/40

Hence the second selling price = 108*100/40 = 270
Option A
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A clock store sold a certain clock to a collector for 20 per 02 Aug 2020, 21:35
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hsk
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
Show more

Let's break this down step by step by translating this from words to math!

"A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock."
C = Cost to Store
X = Sales Price to Collector

X = \(\frac{6}{5}C\)

"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."

\(\frac{1}{2}X\) OR \(\frac{6}{5}*\frac{1}{2}C\) = \(\frac{3}{5}C\)

"The shop then sold the clock again at a profit of 80 percent on its buy-back price." This is probably the "trickiest part to put into words
Remember that: Profits = Sales Prices - Cost
Y = 2nd Time Sales Price

Y - \(\frac{3}{5}C\) = \(\frac{4}{5}*\frac{3}{5}C\)

Y = \(\frac{27}{25}C\)

"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?"
C - \(\frac{3}{5}C\) = 100

C = $250

We are trying to solve for the cost of the second time, plug-in $250 in the
Y = \(\frac{27}{25}C\)

By now you wouldn't have to do the last step because only answer choice A is larger than 250
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A clock store sold a certain clock to a collector for 20 per 19 Nov 2024, 05:27
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Let original cost = x
First sale: x × 1.2 (to collector)
Buy back: x × 1.2 × 0.5 (from collector)
Second sale: x × 1.2 × 0.5 × 1.8 (80% profit)

Given:
x - (x × 1.2 × 0.5) = 100
x - 0.6x = 100
0.4x = 100
x = 250

Final price = 250 × 1.2 × 0.5 × 1.8 = 270
Answer: A
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A clock store sold a certain clock to a collector for 20 per 27 Dec 2025, 19:13
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