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

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

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.

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.

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

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

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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