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An appliance store owner ordered 50 countertop microwave ovens to be

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An appliance store owner ordered 50 countertop microwave ovens to be  [#permalink]

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New post 29 Mar 2018, 22:52
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An appliance store owner ordered 50 countertop microwave ovens to be sold for $144 each, which represents a 20 percent markup over the store owner’s initial cost for each microwave. Of the microwave ovens ordered, 5 were never sold. These ovens were returned for a refund of 50 percent of the owner’s initial cost. What was the owner’s profit or loss as a percent of the initial cost of the 50 microwave ovens?

(A) 15% loss
(B) 13% loss
(C) 10% profit
(D) 13% profit
(E) 15% profit

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Re: An appliance store owner ordered 50 countertop microwave ovens to be  [#permalink]

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New post 29 Mar 2018, 23:05
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Bunuel wrote:
An appliance store owner ordered 50 countertop microwave ovens to be sold for $144 each, which represents a 20 percent markup over the store owner’s initial cost for each microwave. Of the microwave ovens ordered, 5 were never sold. These ovens were returned for a refund of 50 percent of the owner’s initial cost. What was the owner’s profit or loss as a percent of the initial cost of the 50 microwave ovens?

(A) 15% loss
(B) 13% loss
(C) 10% profit
(D) 13% profit
(E) 15% profit


50 ovens

144 = markup of 20% intiial cost = 120

50x120 = 6000 $ (CP)
5 refunded = 300$ refunded
CP = 5700

sp = 45 x 144 ( 5 never sold) =6480

profit

6480-5700/5700 ~13 IMO
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An appliance store owner ordered 50 countertop microwave ovens to be  [#permalink]

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New post 30 Mar 2018, 18:06
Bunuel wrote:
An appliance store owner ordered 50 countertop microwave ovens to be sold for $144 each, which represents a 20 percent markup over the store owner’s initial cost for each microwave. Of the microwave ovens ordered, 5 were never sold. These ovens were returned for a refund of 50 percent of the owner’s initial cost. What was the owner’s profit or loss as a percent of the initial cost of the 50 microwave ovens?

(A) 15% loss
(B) 13% loss
(C) 10% profit
(D) 13% profit
(E) 15% profit

I interpret "initial cost of 50" to mean "cost of 50 before the refund."

You cannot have "initial costs" that account for unsold items before you try to sell the items.

Further, if initial cost does not include refund, the answer is precise, like the answer choices. If the refund is included, the percent is a very messy number.

In calculating profit as a percent of initial cost of 50, therefore, I excluded the refund.

In calculating profit per se, I included the refund.

Initial cost of 50 = (Cost per item, \(c\)) * 50
Cost per item is derived from SP per item = $144
$144 = 20% markup over initial \(c\)
\(1.2c=$144\)
\(c=(\frac{$144}{1.2})=$120\)

Initial cost of 50: \(($120*50) = $6,000\)

Actual cost of 50= ($6,000-$refund)
Refund: 50% of (5*$120)= $600
Refund: (.50 * $600) = $300
Actual cost of 50: ($6,000 - $300) = $5,700

Gross profit: TR - (actual cost of 50)
TR = \((45*$144)=(90*$72)=$6,480\)
Gross profit: \(($6,480-$5,700)=$780\)

Profit as a percent of INITIAL cost of 50?

\(\frac{+780}{6,000}=\frac{39}{300}=\frac{13}{100}*100= +13\) %

Answer D

*My interpretation of "initial cost of 50" as "before refund" is based on syntax, semantics, and answer choices. Syntactically, all three mentions of cost are phrased precisely as "initial cost" (i.e., not the typical phrase, "total cost").

Semantically, it seems odd to include the refund in initial cost. As mentioned, how can we account initially for the number of items that will not sell before they are put on sale? Finally, the answer choices have exact numbers. If the refund is included in "initial cost," profit as a percent of the latter, see below, is an unwieldy number.

If the refund is not included in initial cost, the result is precise, in keeping with the answer choices' numbers. The prompt does not mention approximation.

If initial cost of 50 means "$5,700" the result is messy:
\((\frac{780}{5,700})\approx{.1376}*100\approx{13.76}\approx{13.8}\)%
True, the percent cannot be > 14. Answer (D), +13%, thus is reasonable -- or perhaps just lucky. Interpreting "initial cost of 50" as "inclusive of the refund" may fail to answer the question properly. YMMV
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An appliance store owner ordered 50 countertop microwave ovens to be &nbs [#permalink] 30 Mar 2018, 18:06
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