Tom and Aly purchased a laptop each at the same price

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:

GMAT assassins aren't born, they're made,
Rich

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

Given:
1. Tom and Aly purchased a laptop each at the same price.
2. Both of them marked up the price of their laptops by the same amount.
3. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order;
4. Tom sold his laptop by offering the same scheme of discount but in reverse order.
5. The profit made by Aly was equal to the loss incurred by Tom

Asked: What was the amount of profit (in $) made by Aly?

1. Tom and Aly purchased a laptop each at the same price.
Let the purchase/ cost price of laptop be $x

2. Both of them marked up the price of their laptops by the same amount.
Let the marked up price of laptop be $y

3. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order;
Selling price by Aly = (y-200)80% = .8(y-200) = .8y -160
Cost price = x
Profit gained by Aly = .8y -160 -x (1)

4. Tom sold his laptop by offering the same scheme of discount but in reverse order.
Selling price by Tom = .8y - 200
Loss incurred by Tom = x - (.8y -200) = x - .8y + 200 (2)

5. The profit made by Aly was equal to the loss incurred by Tom
.8y-x-160 = x -.8y+200
.8y - x = 360/2 = 180 (3)

Putting value of .8y-x in (1)
Profit gained by Aly = .8y -160 -x = (.8y-x) - 160 = 180 - 160 = $20

IMO A

Alternatively

The difference in selling price = (.8y-160) - (.8y-200) = $40
Profit (Aly) = Loss (Tom)
Profit + Loss = 40
Profit (Aly) = Loss (Tom) = $20

IMO A

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