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Tom and Aly purchased a laptop each at the same price

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Tom and Aly purchased a laptop each at the same price [#permalink]

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Question Stats:

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Tom and Aly purchased a laptop each at the same price. Both of them marked up the price of their laptops by the same amount. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order; whereas Tom sold his laptop by offering the same scheme of discount but in reverse order. If the profit made by Aly was equal to the loss incurred by Tom, then what was the amount of profit (in $) made by Aly?
(A) $20
(B) $25
(C) $30
(D) $35
(E) $40
[Reveal] Spoiler: OA

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Re: Tom and Aly purchased a laptop each at the same price [#permalink]

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New post 18 Jul 2017, 03:11
TimeTraveller wrote:
Tom and Aly purchased a laptop each at the same price. Both of them marked up the price of their laptops by the same amount. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order; whereas Tom sold his laptop by offering the same scheme of discount but in reverse order. If the profit made by Aly was equal to the loss incurred by Tom, then what was the amount of profit (in $) made by Aly?
(A) $20
(B) $25
(C) $30
(D) $35
(E) $40


Lets say, price after mark up is P.

Sell price of Aly = \((P - 200) 0.8 = 0.8P - 160\)
Sell price of Tom = \(0.8P - 200\)

Since profit of Aly is equal to loss of Tom, we know the actual price lies in the middle and we can split the difference to find the profit/loss made by each.

Difference: \(0.8P - 160 - (0.8P - 200) = 0.8P - 160 - 0.8P + 200 = 40\)

Since this is the added difference from the actual purchase price, we have to halve it to find profit and loss of each.

Profit made by Aly = 20
Loss made by Tom = 20
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Re: Tom and Aly purchased a laptop each at the same price [#permalink]

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New post 18 Jul 2017, 04:20
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TimeTraveller wrote:
Tom and Aly purchased a laptop each at the same price. Both of them marked up the price of their laptops by the same amount. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order; whereas Tom sold his laptop by offering the same scheme of discount but in reverse order. If the profit made by Aly was equal to the loss incurred by Tom, then what was the amount of profit (in $) made by Aly?
(A) $20
(B) $25
(C) $30
(D) $35
(E) $40


Both had to reduce the marked price by $200. The only difference lies in the fact that Aly, since she reduced the amount by 200 first, did not have to give a discount on it. Whereas, Tom gave a 20% off on $200 too i.e. he reduced the price by an extra 20% of 200 = $40

This additional reduction of $40 led to a loss equal to Aly's profit. So Aly must have had $20 profit and Tom must have had $20 loss.

Answer (A)
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Re: Tom and Aly purchased a laptop each at the same price [#permalink]

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New post 20 Jul 2017, 15:46
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TimeTraveller wrote:
Tom and Aly purchased a laptop each at the same price. Both of them marked up the price of their laptops by the same amount. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order; whereas Tom sold his laptop by offering the same scheme of discount but in reverse order. If the profit made by Aly was equal to the loss incurred by Tom, then what was the amount of profit (in $) made by Aly?
(A) $20
(B) $25
(C) $30
(D) $35
(E) $40


We can let p = the price of the laptops when Tom and Aly bought them and m = markup of the laptops. Thus, p + m = the price at which they originally wanted to sell the laptops. However, after the discounts, Aly sold her laptop at the price of (p + m - 200)(0.8) dollars and Tom sold his laptop at the price of 0.8(p + m) - 200 dollars. In dollars, the profit made by Aly is (p + m - 200)(0.8) - p and the loss incurred by Tom is p - (0.8(p + m) - 200). Since Aly’s profit is equal to Tom’s loss, we can create the following equation:

(p + m - 200)(0.8) - p = p - (0.8(p + m) - 200)

0.8p + 0.8m - 160 - p = p - 0.8p - 0.8m + 200

0.8m - 0.2p - 160 = 0.2p - 0.8m + 200

1.6m - 0.4p = 360

16m - 4p = 3600

4p = 16m - 3600

p = 4m - 900

At this point, we actually can make up a number for m (as long as p will be positive). For example, we can let m = 250, so p = 4(250) - 900 = 100. Thus, Aly’s profit is:

(100 + 250 - 200)(0.8) - 100

(150)(0.8) - 100

120 - 100

20 dollars

Note: For any number we make up for m (as long as p will be positive), Aly’s profit will always be $20.

Alternatively, we can substitute p = 4m - 900 in the equation for the profit of Aly:

Profit of Aly = (p + m - 200)(0.8) - p
= (4m - 900 + m -200)(0.8) - (4m - 900)
= (5m - 1100)(0.8) - 4m + 900
= 4m - 880 - 4m + 900
= 20

Answer: A
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Re: Tom and Aly purchased a laptop each at the same price [#permalink]

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New post 03 Dec 2017, 22:01
Hi All,

While this question involves a lot of information to keep track of, we can ultimately solve it by TESTing VALUES (albeit in a slightly "out-of-order" way).

To start, we have no idea what the original price of the laptops were and we don't know what the 'marked up' prices were. I'm going to start with the MARKED UP price and come back to the original price later on:

Marked Up Price = $1,000

Ally sold her laptop after giving a $200 discount, THEN a 20% off discount:
$1,000 - $200 = $800
$800 - (20% of $800) = $800 - $160 = $640

Tom sold his laptop after giving a 20% discount, THEN a $200 off discount:
$1,000 - (20% of $1000) = $1000 - $200 = $800
$800 - $200 = $600

We're told that Ally made a PROFIT that was EQUAL to Tom's LOSS. With sell prices of $640 and $600, respectively, the original purchase price would have had to have been $620

Ally = $640 - $620 = $20 profit
Tom = $600 - $620 = $20 loss

Thus, Ally's profit = $20

Final Answer:
[Reveal] Spoiler:
A


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Re: Tom and Aly purchased a laptop each at the same price   [#permalink] 03 Dec 2017, 22:01
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