Furniture Dealer

[Rudy414]

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and sale of the desk?

$40
$60
$80
$90
$100

Thanks!

[srcc25anu]

Gross profit = sell price - purchase price

if SP = 100, CP = 60 (at 40% mark up on SP)
SO if CP = 150, SP = 100 * 150 / 60 = 250
therefore GP = 250 - 150 = 100
Ans E

[Rudy414]

Can you elaborate on this? I don't follow your logic at all.

If the selling price is $100, as you mentioned, then you don't even need to solve anything. From the problem, would just take the selling price minus the purchase price, which in this case would be $100 - $150 = -$50. Not only is that not an answer, but you could just pick any of the 5 appropriate numbers to satisfy any of the answer choices.

In your solution, what is CP? And if it is the 40% markup of the SP (or $100), wouldn't it equal $140 since 140% of 100 = 140?

Maybe I am missing something. E is the correct answer, but I just don't see how you got there.

[srcc25anu]

Markup of 40% on SP means if SP = 100, markup = 40 and CP is 60
markup means a profit so SP has to be greater than CP.
usually markup is on cost say CP = 100, Markup 40% on cost then SP would be 140

The Q is asking for : what was the markup (in $ terms). we know its 40% of SP but what about if that's to be determined in $ terms.
To know that, we need to know the SP as CP is given ($150). Then markup = GP = SP - cost
And the answer choices are not options for SP, they are infact options for the profit in $ terms.

Hope this is clear.

[GMATGuruNY]

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and sale of the desk?

$40
$60
$80
$90
$100

Thanks!

We can plug in the answers, which represent the profit.
When the current answer choice is plugged in, the profit must be equal to the markup.

Answer choice C: profit = 80.
Selling price = profit + purchase price = 80+150 = 230.
Markup = 40% of the selling price = .4(230) = 92.
Since the profit is less than the markup, the profit must increase.
Eliminate A, B and C.

Answer choice D: profit = 90.
Selling price = profit + purchase price = 90+150 = 240.
Markup = 40% of the selling price = .4(240) = 96.
Since the profit is less than the markup, the profit must increase.
Eliminate D.

The correct answer is E.

Note that we had to try only 2 answer choices, an efficient way to determine the correct answer.

Answer choice E: profit = 100.
Selling price = profit + purchase price = 100+150 = 250.
Markup = 40% of the selling price = .4(250) = 100.
Profit = markup = 100.
Success!

Algebraically:
Let m = markup.
Selling price = purchase price + markup = 150 + m.
Markup = 40% of the selling price = .4(150+m).
Since m = markup and markup = .4(150+m), we get:
m = .4(150 + m)
10m = 4(150+m)
10m = 600 + 4m
6m = 600
m = 100.