Official Guide13 - PS Q#182 Percent

[sps1604]

[/quote] Q#182 A photography dealer ordered 60 model X cameras to be sole for $250 each, which represents a 20 percent markup over the dealer's initial cost for each camera. Of the camera ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of dealer's initial cost. What was dealer's approximate profit or loss as a percent of the dealer's initial cost of 60 cameras?

I solved the question as follows :-

Dealer's Initial cost of camera = x
x+ x/4 = 250
5x/4=250
Hence, x= 200 with markup price as 25

Revenue earned after selling = 54*250 = 13500
Cost incurred = 60*200 - 6*100 = 11400

Profit % = 2100/11400 *100

Please help me understand, where did I go wrong!

[bubbliiiiiiii]

Dealer's Initial cost of camera = x
x+ x/4 = 250 x/4 represents 25 % whereas profit is 20%. So you should have use x/5 to find cost price
5x/4=250


Please help me understand, where did I go wrong![/quote]

[bubbliiiiiiii]

Is the answer apprx. equal to 13.7 % Profit?

[sps1604]

Is the answer apprx. equal to 13.7 % Profit?

Yes, the answer is 13% profit. Thanks for pointing out my mistake!

[GMATGuruNY]

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

54 cameras yield a 20% profit, while 6 cameras suffer a 50% loss.
Average for all 60 cameras = (54*20 - 6*50)/60 = 780/60 = 13.

The correct answer is D.

[Brent@GMATPrepNow]

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

I think Mitch's solution using weighted averages is, by far, the best way to go here. However, if you didn't spot that approach, it's important to recognize that we really don't need to use the information about the cameras selling for $250 each. The question boils down to . . .

54 cameras were sold at a 20% markup, and cameras were sold at a 50% markdown. What was the approximate profit or loss as a percent of the dealer's initial cost for all 60 cameras?

So, we can assign an easy value of $100 to the initial cost per camera.
This means the 60 cameras cost $6000 to buy.

54 cameras were sold at a 20% markup and 6 cameras were sold at a 50% markdown.
So, 54 cameras were sold for $120, and 6 cameras were sold for $50.
(54)($120) + (6)($50) = $6780
So, the cameras were sold for $6780

This represents a profit of $780

If the initial cost was $6000, we must determine the percentage equivalent to $780/$6000

$780/$6000 = 78/600 = 13/100 = 13%

Answer = D

Cheers,
Brent

[adt29]

I think Mitch's solution using weighted averages is, by far, the best way to go here.

Brent and Mitch,
A little slow here: how do you think of weights in this problem? Are the weights the percents (20% markup and then 50% loss)? if that's the case, then according to the weighted avg formula, the denominator should be a sum of the weights right? how do you know to divide by 60?

Thanks in advance for your help!

[Brent@GMATPrepNow]

I think Mitch's solution using weighted averages is, by far, the best way to go here.

Brent and Mitch,
A little slow here: how do you think of weights in this problem? Are the weights the percents (20% markup and then 50% loss)? if that's the case, then according to the weighted avg formula, the denominator should be a sum of the weights right? how do you know to divide by 60?

Thanks in advance for your help!

Here's Mitch's solution:
Average for all 60 cameras = (54*20 - 6*50)/60 = 780/60 = 13

This is the same as:
Average for all 60 cameras = (54/60)20 + (6/60)(-50)
So, 54/60 of the inventory solve for a 20% profit
To this, we add the fact that 6/60 of the inventory solve for a 50% loss

I hope that helps.

Cheers,
Brent

[GMATGuruNY]

We can simplify the arithmetic even further if we realize the following.
(54 sold)/(6 not sold) = (9 sold)/(1 not sold).

Thus, of every 10 cameras, 9 earn a 20% profit, while 1 suffers a 50% loss.
Thus, the average profit/loss for every 10 cameras = (9*20 - 1*50)/10 = 13.