A photography dealer ordered 60 Model X cameras to be sold

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.

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

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.

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

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.

This formula is an application of the scale method:

\(\frac{w1}{w2} = \frac{A2 - Aavg}{Aavg - A1}\)

It is faster and more direct than actually using the number line.

My thought process with very similar with akang. After reading the problem, I just saw "percent", "percent" "What percent...?" So I didn't even bother with the marked-up "$250"

In my head, I saw:

(6 out of 60) = 10% of stuff (never sold, returned, = loss) at 50% loss

(rest of stuff, not 6, minus 10%) = 90% of stuff (gives him 20% markup) at 20% profit

And his T (total) whatever percentage is Profit - Loss

So, my scratch paper for this problem literally looks like:

90% of 20% = 18%
10% of 50% = 5%
P - L = ___________

18% - 5% = 13%

Then I thought, "profit" since the gain was bigger than the loss.

The other clue to ditch the $250 and any other non-percentages was when I tried to figure out the actual cost per camera. When I tried to divvy up 250 by 1.2 and started to get something funky, I thought, "Ok, they don't want me to mess with that."

Right? So is my thought process applicable to other problems like this? We don't actually have to mess with actual total profit and dividing by huge numbers to get the answer, huh? Or am I narrowing my train of thought down too much that it will only work for this problem? And I totally feel you on the weighted averages equation, but is it a good habit to use weighted averages for all problems like this? Do we need the full meal deal, or can I get away with just the burger?

I just think it's funny when I see contributors online write out work like: "1,644/12,480 = ~13%. See?" As if were all supposed to be like, "Oh, of course! Divided by twelve thousand four hundred and eighty IS about thirteen percent. Makes total sense." Like us normal people could just come up with that answer that easily and that quickly, without a calculator, during the actual test. No offense to anyone, I love this site, but I already have the answers in the back of the book. What helps, at least, helps me, is when I can be shown how to break the work down into small digestible pieces that can be used on other questions as well. Like eating cookies in bed. The trick is to break them up inside the bag, then put the small cookie pieces in your mouth. No crumbs all over the sheets.

But maybe that's just me.

Thanks everyone.

Responding to a pm - a useful tip for everyone:



Don't try to calculate the reverse percentage lest you make a mistake. Use the straight forward percentage manipulation even if that needs a variable. Even if you do not want to actually write it down, make a straight forward equation in your mind like this:

Cost * (6/5) = 250

So
Cost = 250 * (5/6)

This question can be solved using the concept of weighted average.

Good cameras = 54 (Profit of 20%)
Bad cameras = 6 (Loss of 50%)

Method 1: - The long way:

SP of each camera is 120% of the cost
=> Cost of each camera = $(250/1.2) = $(1250/6)
Total cost = (1250/6) x 60 = $12500
SP from 54 cameras = 250 x 54 = $13500
The remaining 6 cameras were returned for half the cost price, i.e. (1250/6)/2 = $(625/6)
Price obtained from these 6 = 6 x 625/6 = $625
Total SP = 13500 + 625 = $14125
Profit % = (14125 - 12500)/12500 x 100 = 13%

Method 2: - The short way:

In questions that ask for percent profit, the actual values aren't required - we just need to know the ratio of the prices and the ratio of the quantities
54 cameras were sold at some profit and the remaining 6 were returned, incurring a loss => the quantity ratio is 54 : 6 = 9 : 1
The 54 cameras were sold at 20% profit and the 6 were effectively sold at 50% loss

Thus, the net percent profit or loss can be simply obtained by a weighted average (note that all cameras have the same CP):

\(\frac{[9 * 20 + 1 * (-50)]}{(9 + 1)}\) = 13%

Answer B

Given: 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.

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

Dealer's initial cost of each camera = $250/1.2

Dealer's initial cost of 60 cameras = $250/1.2 * 60 = $12500

Total sales of 60 cameras = (60-6)*$250 + 6*50%*$250/1.2 = $14125

Percentage profit on 60 cameras = ($14125 - $12500) / $12500 * 100% = 13%

IMO D

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.

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!

Hey all,
Why do we divide 250/2.4? Where does 2.4 come from?
Thanks!

Cost to dealer = 250/1.2 (because 250 is the selling price which 20% markup)

Revenue from the 6 cameras is half the cost price. This is = (250/1.2)*(1/2) = 250/2.4

P.S. - Saw your post later Engr2012

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'.