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705-805 Level|   Percent and Interest Problems|                                 
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A photography dealer ordered 60 Model X cameras to be sold Updated on: 09 Jul 2021, 00:34
Originally posted by pgmat on 06 May 2012, 10:53.
Last edited by Bunuel on 09 Jul 2021, 00:34, edited 1 time in total.
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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
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D
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A photography dealer ordered 60 Model X cameras to be sold Updated on: 16 Nov 2023, 22:51
Originally posted by KarishmaB on 24 Jun 2012, 22:20.
Last edited by KarishmaB on 16 Nov 2023, 22:51, edited 3 times in total.
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pgmat
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
Show more

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

Here is a video solution to this problem: https://youtube.com/shorts/gDLtpsK-SOI

Read more about the weighted average concept here: https://anaprep.com/arithmetic-weighted-averages/
and watch this video: https://www.youtube.com/watch?v=_GOAU7moZ2Q
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A photography dealer ordered 60 Model X cameras to be sold Updated on: 25 Feb 2016, 08:28
Originally posted by MBAhereIcome on 23 Jun 2012, 07:31.
Last edited by MBAhereIcome on 25 Feb 2016, 08:28, edited 1 time in total.
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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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A photography dealer ordered 60 Model X cameras to be sold 06 May 2012, 11:07
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pgmat
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
Show more

The total cost = 60*($250/1.2) = 50*250;

The number of cameras sold = 60 - 6 = 54.
The total revenue = $54*250;

The number of cameras returned = 6.
The total refund = $6*(250/1.2)*0.5;

So, the total income = $54*250+ 6*(250/1.2)*0.5

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

Answer: D.
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A photography dealer ordered 60 Model X cameras to be sold 16 Nov 2012, 23:48
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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 :)
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actually, if one could visualize this problem properly, it could be solved in less than 30 secs without getting into any dirty calculations.
Here is my 30 sec approach:
Notice that it is actually a wighted ratio problem, where 9 parts earned 20% profit and 1 part earned 50% loss. (54 for profit, 6 for loss).
Hence overall profit/loss = \((9*20 -1*50) /(9+1) = 13\)
Ans D it is!
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A photography dealer ordered 60 Model X cameras to be sold 16 Nov 2012, 23:15
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carcass
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 :)
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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%

Answer is D.

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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A photography dealer ordered 60 Model X cameras to be sold 22 Jun 2012, 14:14
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Bunuel
pgmat
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.
Show more

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?
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A photography dealer ordered 60 Model X cameras to be sold 23 Jun 2012, 04:06
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kashishh
Bunuel
pgmat
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.

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?
Show more

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.
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A photography dealer ordered 60 Model X cameras to be sold 24 Jun 2012, 02:06
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MBAhereIcome
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.
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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.
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A photography dealer ordered 60 Model X cameras to be sold 24 Jun 2012, 12:26
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gmatDeep
MBAhereIcome
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.
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yess.. 54:6 = 9:1
mark up is of 20% = profit earned will be 20%
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A photography dealer ordered 60 Model X cameras to be sold 16 Nov 2012, 23:27
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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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A photography dealer ordered 60 Model X cameras to be sold 24 Nov 2012, 11:16
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Hi,

For those using normal way to solve this problem, I think that we can avoid huge calculation by just replace Cost by letter C and put it in the final formula:
Income: 54*1.2C + 6*0.5C
Cost: 60*C
Then percent =(Income-cost)/cost = (54*1.2C + 6*0.5C - 60*C)/60*C. We can see that we can eliminate C from the fraction --> percent = (54*1.2 + 6*0.5 - 60)/60 = (54*1.2 + 6*0.5)/60 - 1. Here, we can see clearly the weighted average part of the problem or we can simply calculate the fraction to reach the result.
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A photography dealer ordered 60 Model X cameras to be sold 27 May 2013, 12:12
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Bunuel
pgmat
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.
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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;"
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A photography dealer ordered 60 Model X cameras to be sold 27 May 2013, 12:19
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Bunuel
pgmat
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;"
Show more

(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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A photography dealer ordered 60 Model X cameras to be sold 07 Apr 2014, 19:23
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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.
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A photography dealer ordered 60 Model X cameras to be sold 27 May 2014, 10:33
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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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A photography dealer ordered 60 Model X cameras to be sold 21 Aug 2014, 08:48
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VeritasPrepKarishma
pgmat
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/
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why are we dividing by 10?
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A photography dealer ordered 60 Model X cameras to be sold 24 Aug 2014, 21:54
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pgmat
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/
why are we dividing by 10?
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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.
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A photography dealer ordered 60 Model X cameras to be sold 18 Apr 2015, 02:29
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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.
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A photography dealer ordered 60 Model X cameras to be sold 22 Apr 2015, 05:13
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Andrewbpaa
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.
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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
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