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# A photography dealer ordered 60 Model X cameras to be sold

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A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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06 May 2012, 10:53
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A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? A. 7% loss B. 13% loss C. 7% profit D. 13% profit E. 15% profit [Reveal] Spoiler: OA Kudos [?]: 177 [6], given: 8 Senior Manager Status: mba here i come! Joined: 07 Aug 2011 Posts: 261 Kudos [?]: 1227 [69], given: 48 A photography dealer ordered 60 Model X cameras to be sold [#permalink] ### Show Tags 23 Jun 2012, 07:31 69 This post received KUDOS 26 This post was BOOKMARKED 54 cameras gave 20% profit while 6 incurred 50% loss. or out of 10, 9 gave profit. suppose total cameras = 10 and each costs$10
total profit = $2*9 -$5*1 = $13 or 13% (with$100 cost)
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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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pgmat wrote:
A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? A. 7% loss B. 13% loss C. 7% profit D. 13% profit E. 15% profit Use weighted avgs for a quick solution: On 54 cameras, the dealer made a 20% profit and on 6 cameras, he made a 50% loss. Cost Price of 54 cameras:cost price of 6 cameras = 54:6 = 9:1 Avg Profit/Loss = (.2*9 + (-.5)*1)/10 = 1.3/10 = .13 = 13% profit For more on weighted avgs, check: http://www.veritasprep.com/blog/2011/03 ... -averages/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Of the cameras ordered, 6 were never sold and were returned [#permalink]

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carcass wrote:

A. 7% loss
B. 13% loss
C. 7% profit
D. 13% profit
E. 15% profit

Total cost 60*($250/1.2)=50*250; # of cameras sold is 60-6=54 total revenue is 54*250; # of cameras returned is 6 total refund 6*(250/1.2)*0.5; So, total income 54*250+ 6*(250/1.2)*0.5 The dealer's approximate profit is (54*250+ 6*(250/1.2)*0.5-50*250)/(50*250)*100=13% Answer: D. _________________ Kudos [?]: 129127 [16], given: 12194 Moderator Joined: 02 Jul 2012 Posts: 1216 Kudos [?]: 1663 [12], given: 116 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Of the cameras ordered, 6 were never sold and were returned [#permalink] ### Show Tags 16 Nov 2012, 23:15 12 This post received KUDOS 3 This post was BOOKMARKED carcass wrote: A photography dealer ordered 60 Model X cameras to be sold for$250 each, whichrepresents a 20 percent markup over the dealer's initialcost for each camera.
Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer's initial cost for the 60 cameras?

(A) 7% loss

(B) 13% loss

(C) 7% profit

(D) 13% profit

(E) 15% profit

have fun. is not difficult to conceptualize but is difficult because if you are not organized and clear you are get in trouble.

I would not show the OA but the rules are stringent. either way try on your own

Cost to dealer for 60 cameras = $$\frac{250}{1.2}*60$$ = $12,500 Revenue for 54 cameras = 54*250 =$13,500

Revenue from 6 cameras = $$\frac{250}{2.4}*6$$ = $625 Total Revenue =$14,125

Profit percent = $$\frac{14125-12500}{12500}$$ = 13%

Otherwise, If one were short on time and I had to guess, One can eliminate A,B & C by looking at the problem itself and improve my chances of guessing the right answer to 50% between D & E.

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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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23 Jun 2012, 04:06
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kashishh wrote:
Bunuel wrote:
pgmat wrote:
A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? A. 7% loss B. 13% loss C. 7% profit D. 13% profit E. 15% profit Total cost 60*$250/1.2=50*250;

# of cameras sold is 60-6=54 total revenue is 54*250;
# of cameras returned is 6 total refund 6*(250/1.2)*0.5;
So, total income 54*250+ 6*(250/1.2)*0.5

The dealer's approximate profit is (54*250+ 6*(250/1.2)*0.5-50*250)/(50*250)*100=13%

Dear Bunuel,
Ths is a doubt i face with %ages, in ths quest too.
could you pls tell where i m going wrong?
when 20% mark up for initial cost is given , how to calculate it?
250 - 20/100*250 or to take if 120 is 250 then how much is 100?
how have you arrived at 1.2?

If it's given that the selling price is $250 and the markup over the initial cost is 20%, then: {Cost}+0.2{Cost}=1.2*{Cost}={Selling price} --> 1.2*{Cost}=$250 --> {Cost}=$250/1.2. Hope it's clear. _________________ Kudos [?]: 129127 [3], given: 12194 Math Expert Joined: 02 Sep 2009 Posts: 41894 Kudos [?]: 129127 [3], given: 12194 Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink] ### Show Tags 27 May 2013, 12:19 3 This post received KUDOS Expert's post FTGNGU wrote: Bunuel wrote: pgmat wrote: A photography dealer ordered 60 Model X cameras to be sold for$250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?

A. 7% loss
B. 13% loss
C. 7% profit
D. 13% profit
E. 15% profit

Total cost 60*($250/1.2)=50*250; # of cameras sold is 60-6=54 total revenue is 54*250; # of cameras returned is 6 total refund 6*(250/1.2)*0.5; So, total income 54*250+ 6*(250/1.2)*0.5 The dealer's approximate profit is (54*250+ 6*(250/1.2)*0.5-50*250)/(50*250)*100=13% Answer: D. this must be kind of awkward question but i got no option other than asking you. 20% markup over the dealer’s initial cost for each camera- I made a wrong assumption , but reducing 20%from 250 & got 200 as an initial cost for each. please explain that "Total cost 60*($250/1.2)=50*250;"

(Cost per unit) + 0.2*(Cost per unit) = $250 1.2*(Cost per unit) =$250
(Cost per unit) = $250/1.2 Total cost for 60 units = 60*(Cost per unit) = 60*($250/1.2) = 50*250.

Hope it's clear.
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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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Because the answers are in percentages, I thought not to worry about the $amounts and just focus on the relationships: Let C be the total cost of all 60 cameras. Originally, the dealer thought to sell all these 60 cameras at 20% profit or for (1.2)C. However, he sold only (60-6)=54 or 90% of cameras at this price. So revenue from these cameras = (0.9)(1.2)C = (1.08)C For the remaining 10%, he got a refund of 50% of cost or (0.5)C. So total refund = (0.1)(0.5)C = (0.05)C Therefore, total revenue in terms of original cost = (1.08 + 0.05)C = 1.13C or 13% profit. So D is the correct ans. Kudos [?]: 18 [3], given: 16 Intern Joined: 28 Feb 2012 Posts: 22 Kudos [?]: 12 [1], given: 3 GMAT 1: 700 Q48 V39 WE: Information Technology (Computer Software) Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink] ### Show Tags 24 Jun 2012, 02:06 1 This post received KUDOS MBAhereIcome wrote: 54 cameras gave 20% profit while 6 incurred 50% loss. or out of 10, 9 gave profit. suppose total cameras = 10, out of which 9 gave 20% profit suppose 100 was the cost of each. total profit 100*10=1000 profit from 9 = 20*9 = 180 loss from 1 = 50*1 = 50 total profit = 180-50 = 130 so, 130 profit from a cost of 1000. that is 13% profit. Your method seems easy, but I kind of got lost with this - 54 cameras gave 20% profit while 6 incurred 50% loss. or out of 10, 9 gave profit. Could you please explain, how you deduced this? Thanks. Kudos [?]: 12 [1], given: 3 VP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1347 Kudos [?]: 643 [1], given: 20 GMAT 1: 780 Q51 V48 GRE 1: 1540 Q800 V740 Re: Of the cameras ordered, 6 were never sold and were returned [#permalink] ### Show Tags 16 Nov 2012, 23:27 1 This post received KUDOS 60 cameras were ordered to be sold at a 20% markup for$250 each
=> Dealer's cost for each camera = $208 => Cost of all 60 cameras =$60*208

6 cameras were not sold and returned for a refund of 50% of the dealer's cost
=> The amount the dealer got in returns = 50% of 6*208 = $624 The rest of the cameras (60-6 = 54 in number) were sold => Revenue made from selling the cameras =$54 * 250

For the 60 cameras, dealer's profit = 100* [54*(250-208) + (624-1248)]/[(60*200)] =100* (14100-12000)/12000 = ~13% (the error arises because 250/1.2 is not exactly 208 but 208.33)

Option (D)
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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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{(54*20) + (6*(-50))}/ 60

This gives 13% profit as answer. 20% proft on 54 cameras and 50% loss on 6 cameras. Use weighted averages here. Rest of the information in the question is misguiding.

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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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24 Aug 2014, 21:54
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sagnik242 wrote:
VeritasPrepKarishma wrote:
pgmat wrote:
A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? A. 7% loss B. 13% loss C. 7% profit D. 13% profit E. 15% profit Use weighted avgs for a quick solution: On 54 cameras, the dealer made a 20% profit and on 6 cameras, he made a 50% loss. Cost Price of 54 cameras:cost price of 6 cameras = 54:6 = 9:1 Avg Profit/Loss = (.2*9 + (-.5)*1)/10 = 1.3/10 = .13 = 13% profit For more on weighted avgs, check: http://www.veritasprep.com/blog/2011/03 ... -averages/ why are we dividing by 10? Weighted Average Formula: Cavg = (C1*w1 + C2*w2)/(w1 + w2) C1 and C2 represent the quantity which we want to average so they will be profit/loss here. C1 = 20% = .2 C2 = -50% (loss) = -.5 The weights, given by w1 and w2, are the cost prices. Cost Price of 54 cameras:cost price of 6 cameras = 54:6 = 9:1 So w1 =9 and w2 = 1 Avg Profit/Loss = (.2*9 + (-.5)*1)/(9 + 1) = (.2*9 + (-.5)*1)/10 Get more details on this concept from the link given in my post above. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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22 Apr 2015, 05:13
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Andrewbpaa wrote:
Suppose: what if I want to calculate the number of the total profit first. How can I get it? I tried to get it by "54^250/1.2. Is this is the correct way? Pls enlighten. Thanks in advance.

Hi Andrewbpaa,

For calculating the total net profit, you would need to know the cost price and the selling price of all the 60 cameras:

On a selling price of $250, the dealer makes a profit of 20%. So, his cost price for 1 camera would be $$= \frac{250}{1.20}$$ His refund price for 6 cameras is 50% of his cost price i.e. $$0.5* \frac{250}{1.20}$$ I. Profit from selling 54 cameras at$250 each$$= 54 * (  250 - \frac{ 250}{1.20})$$
II. Loss from refund of 6 cameras = $$6 *( \frac{250}{1.20} - \frac{ 250}{1.20} * 0.50)$$ $$= 6*( \frac{250}{1.20} * 0.50)$$

Adding I & II would give you the total net profit the dealer made on the 60 cameras. The net profit can then be divided by the total cost price of 60 cameras to arrive at the total profit% of the dealer.

However, I would suggest you use weighted average method to solve the question.

Points to Note
In such questions, it pays to be careful about the concept of markup% and discount%. In this question, there was no discount offered, hence the markup price and selling price were the same i.e. $250. Had there been a discount of lets say 10%, the selling price would have been $$250* 0.9 = 225$$. The profit then would have been equal to $$225 - \frac{ 250}{1.20}$$ Please remember that the markup% is calculated on the cost price while the discount % is calculated on the markup price. Given below are few questions on discount & markup for your practice: if-the-original-price-of-an-item-in-a-retail-store-is-marked-163706.html?hilit=discount a-pair-of-skis-originally-cost-160-after-discount-of-x-149918.html a-jewelry-dealer-initially-offered-a-bracelet-for-sale-at-an-8215.html?hilit=discount%20&%20markup henry-purchased-three-items-during-a-sale-he-received-a-20-discount-194280.html?hilit=discount Hope its clear! Regards Harsh _________________ | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com Kudos [?]: 2089 [1], given: 123 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7676 Kudos [?]: 17380 [1], given: 232 Location: Pune, India Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink] ### Show Tags 06 Sep 2015, 20:58 1 This post received KUDOS Expert's post bablu1234 wrote: A big question I have is, why does following method give different answer though I believe there is no flaw in my method of attempting this problem - Purchase price per camera = 250/1.2 = 1250/6. Total purchase price = 60 * 1250/6 = 12500$

Got return money because of 6 cameras which were returned = 50% of 6 = [(6 * 250/1.2)/2] = 625$Effective purchase price = 12500 - 625 = 11875$

Total sale = 54 * 250 = 13500$. Hence % profit = [(Total sale - effective purchase price) / (effective purchase price)] x 100 = [(13500 - 11875) / 11875] x 100 = (1625/11875) x 100 = 13.684 Ans. Dealer paid total cost of 60 cameras and then I deducted 50% cost of 6 cameras from that instead of adding it as a revenue. So in this case, technically 54 cameras have been sold and 57 were bought. Can anyone explain why can't I do that way? TIA You have assumed the situation to be a bit different from what it actually is. You have assumed that he bought 54 cameras at 250/1.2 each and 6 cameras at 125/1.2 each. Then he sold 54 cameras at 250 each and 6 cameras at 0. While actually this is the situation: He bought 60 cameras at 250/1.2 each. He sold 54 at 250 each and sold the rest of the 6 at 125/1.2 each. The difference (Revenue - Cost) in both cases will be the same but the cost price in the denominator will be different. So profit % obtained will be different. Please check Bunuel's solution on Page 1 to see the actual calculations of this method. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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sagnik242 wrote:
VeritasPrepKarishma wrote:
pgmat wrote:
A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? A. 7% loss B. 13% loss C. 7% profit D. 13% profit E. 15% profit Use weighted avgs for a quick solution: On 54 cameras, the dealer made a 20% profit and on 6 cameras, he made a 50% loss. Cost Price of 54 cameras:cost price of 6 cameras = 54:6 = 9:1 Avg Profit/Loss = (.2*9 + (-.5)*1)/10 = 1.3/10 = .13 = 13% profit For more on weighted avgs, check: http://www.veritasprep.com/blog/2011/03 ... -averages/ why are we dividing by 10? The weights are 54 (20% profit on 54 cameras) and 6 (50% loss on 6 cameras). This is a ratio of 54:6 = 9:1 (in lowest terms). It is the same thing whether you use 54 and 6 as weights or 9 and 1 but 9 and 1 simplify the calculations. Avg = (A1 * w1 + A2 * w2)/(w1 + w2) = (A1 * 9 + A2 * 1)/(9 + 1) = (A1 * 9 + A2 * 1)/10 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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01 Mar 2016, 23:48
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philipb wrote:
Does this question bother anyone else in formatting terms? Perhaps I'm misinterpreting, but let me explain:

"What was the dealer's approximate profit or loss as a percent of the dealer's initial cost for the 60 cameras?"

Profit = Revenue - Costs

Thus, the question is looking for (Revenue - Cost) / Cost

In number terms this would look like, [54*(250) + 6*(250)*(4/5)*(1/2) - 600*(250)*(4/5)]/[(60)*(250)*(4/5)]x100 ~~ 10.7%

I'd appreciate any help in clearing up this misunderstanding!

You are correct conceptually.

The error lies here:

"$250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera." Marked price is 250 This is a 20% markup on cost. Cost * (1 + 20/100) = Marked price Cost * (6/5) = Marked Price Cost = (5/6) * 250 You have taken this to be (4/5)*250. Replace it by (5/6) and you should get the correct answer. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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05 Mar 2016, 23:56
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Two words: "weighted average"

[ 1.2(54) + 0.5(6) ] / 60 = 67.8 / 60 = 1.13.

Hence, 13% profit.

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Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink]

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13 Mar 2017, 01:43
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Cost of each camera would be $250/1.2 =$208.33
total cost of 60 cameras would be 60*$208.33$12500
Actual number of cameras sold is 6 less i.e 54
revenue generated 54*250
no of cameras returned 6 so refund cost is $6*208.3*50% So, total income 54*250+ 6*($208.33)*50%

The dealer's approximate profit is (54*250+ 6*($208.33)*0.5-50*250)/(50*250)*100=13% Kudos [?]: 33 [1], given: 10 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7676 Kudos [?]: 17380 [1], given: 232 Location: Pune, India Re: A photography dealer ordered 60 Model X cameras to be sold [#permalink] ### Show Tags 03 Apr 2017, 00:17 1 This post received KUDOS Expert's post diegocml wrote: VeritasPrepKarishma wrote: pgmat wrote: A photography dealer ordered 60 Model X cameras to be sold for$250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?

A. 7% loss
B. 13% loss
C. 7% profit
D. 13% profit
E. 15% profit

Use weighted avgs for a quick solution:

On 54 cameras, the dealer made a 20% profit and on 6 cameras, he made a 50% loss. Cost Price of 54 cameras:cost price of 6 cameras = 54:6 = 9:1

Avg Profit/Loss = (.2*9 + (-.5)*1)/10 = 1.3/10 = .13 = 13% profit

For more on weighted avgs, check: http://www.veritasprep.com/blog/2011/03 ... -averages/

VeritasPrepKarishma, I think you method is pretty sweet - I just used another weighted average looking formula you shared in your blog:

$$\cfrac { w1 }{ w2 } :=\cfrac { \left( A2-Aavg \right) }{ \left( Aavg-A1 \right) } =\\ =\cfrac { 1 }{ 9 } =\cfrac { \left( 1.2-Aavg \right) }{ \left( Aavg-0.5 \right) } \\ =Aavg-0.5=9\left( 1.2-Aavg \right) \\ =Aavg-0.5=10.8-9Avg\\ =Aavg+9Aavg=10.8+0.5\\ =10Aavg=11.3\\ =Aavg=\cfrac { 11.3 }{ 10 } \\ Aavg=1.13$$

13% profit

I'm a big fan of the scaled method but I can't figure out how to set it up as to find the 'combined average'.

Yes, you have used the scale method successfully to find the average sale price.
Assuming cost price of each camera is 1, 1.2 is the sale price of 54 cameras and .5 is the sale price of 6 cameras.
Hence you get the average sale price as 1.13.

Scale method is also depicted by the formula you used.

You can use the same formula with profit/loss percent and get the same answer.

w1/w2 = (A2 - Aavg)/(Aavg - A1)

1/9 = (20 - Aavg)/(Aavg - (-50))

Aavg + 50 = 9*(20 - Aavg)

10*Aavg = 130

Aavg = 13

Just that, when I have to find the average, I prefer to use the formula in the form

Aavg = (A1*w1 + A2*w2)/(w1 + w2)

It is just a realignment of the previous formula.
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Re: A photography dealer ordered 60 Model X cameras to be sold   [#permalink] 03 Apr 2017, 00:17

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