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
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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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com