An electronics store purchased a CD player at a wholesale price of 60$

Hi,
here we just have to be careful what should be the BASE on which profit is being calculated..

WP = 60
ORP = R
Selling Price =S= 0.6R
% profit on \(WP = 25% = \frac{(0.6R-60)}{60} *100\)
R = 125..
Profit = 0.6R-60 = 75-60=15..

Profit as a percent of the original retail price =\(\frac{15}{R}*100 = \frac{15}{125}*100 =12\)
B
_________________

let me set up the equations again and bring the answer for u

BTW answer is 12%

cost price =$60
let actual retail price be R(the above price is not retail , its wholesale so don't confuse )
Retail price > Whole sale price(always)

so 40%discount on R =0.6R(selling price of th product )

so question says

selling price -cost price=profit

0.6R -60=25% of 60(whole sale price as per question)=15

R=125

question asks ( profit/actual retail price ) *100

15/125 *100=12%

We'll talk in percentage terms and use the good ol' unitary method..

Let Wholesale Price be p and Retail Price be r..

\(125p = 60r\)

The profit is 25% of p.
Thus, by using unitary method..

\(125p =60r\)

--> \(25p = 60*\frac{25}{125}*r\)

-->\(25p = 12r\)

Answer..12%(B)

Please explain how R=125 ?


Let me try to explain you as best as possible,

wholesale price of CD player 60$
Add:25 percent profit on the whole price
= Selling Price of the Store = $60+ $15 (25% profit)= $75


Now it is given that the store sold at 40% discount of the original price. So let original Price be $100(assumption: because percent is involved).
less= 40% discount = 100-40%= $60 (selling price to the store)

When the selling price to the store is $60 then original price is 100. there fore when selling price to the store is $75, the original price is?

100*75 = $125
60

Now the profit is $15 and original price is $125. SO the percent profit of original price is
$15*100 = 12%
$125

Let original retail price = r, Given wholesale price = $60

r (original retail price) --> (purchased at wholesale price) $60 --> sold at 40% discount of original retail price i.e. (r*60/100)

Store made 25% profit on WHOLESALE price: ((selling price – wholesale price)/wholesale price) *100 = 25

=> ((0.6r-60)/60)* 100 = 25 => r = 125

$125 (original) --> $60 (wholesale) --> $75 (selling price)

Store Profit = 75-60 = $15
Profit as a percent of original retail price = (15/125)*100 = 12 %

I did this one a bit differently, using the Profit = Revenue - Cost formula.


"The store made a 25% profit on the wholesale price of the CD"

\(Profit = \frac{1}{4} * Wholesale Price\)

Profit = 15

Now, the only cost given is the wholesale price of $60, so using the P = R - C formula above gives:

Profit = Revenue - Cost
$15 = Revenue - $60
Revenue = $75

The crux of the problem comes in recognizing that the revenue, $75, is the selling price, which is a 40% discount from the original retail price. Translating this gives:

75 = 60% * OriginalPrice

\(OriginalPrice = \frac{75*5}{3}\)
\(OriginalPrice = 25 * 5\)
\(OriginalPrice = 125\)

Finally, the question asks us to find the store's profit as a percent of the original price. This can be translated as:

\(\frac{x}{100}\)= \(\frac{Profit}{OriginalPrice}\)
\(\frac{x}{100}\) = \(\frac{15}{125}\)
\(\frac{x}{100}\) = \(\frac{3}{25}\) <-- (multiply numerator and denominator by 4)
\(\frac{x}{100} = \frac{12}{100}\)

x = 12

Ans B

We are given that the cost of the CD player was 60 dollars and that the store sold it at a 40 percent discount off the original retail price. If we let x = the original retail price, then the store sold the CD player for 0.6x dollars. Since the store made a 25% profit on the wholesale price, it made 0.25(60) = 15 dollars of profit. Since revenue - cost = profit, we can create the following equation:

0.6x - 60 = 0.25(60)

0.6x - 60 = 15

0.6x = 75

x = 125

So the profit as a percent of the original retail price is:

15/125 x 100 = 0.12 x 100 = 12 percent.

Answer: B
_________________

Hi All,

Since the answer choices in this question are relatively close together, you have to be careful about the math 'work' that you do - and make sure that you label all of your work so that you don't get lost in all of the details in this prompt...

We're told that a CD player had a wholesale price of $60 and that it was sold at 40% off the RETAIL PRICE...

Retail Price = X
Wholesale Price = 60
Actual Sell Price = X - .4X = .6X

The store made a 25% profit on the WHOLESALE price, so...

Actual Sell Price = 60 + .25(60) = 60 + 15 = 75
.6X = 75
X = 75/.6 = 750/6 = 125

So....
Retail Price = $125
Wholesale Price = $60
Actual Sell Price = $75
Profit = $15

We're asked for the PROFIT as a percent of the RETAIL PRICE... (15)/(125) = 3/25 = 12%

Final Answer:

GMAT assassins aren't born, they're made,
Rich

An electronics store purchased a CD player at a wholesale price of 60$ and then sold it at a 40 percent discount off the original retail price. If the store made a 25 percent profit on the wholesale price of the CD player, what was the store's profit as a percent of the original retail price?

This is a good question that tests the candidate in understanding the concept of profit and loss. Also, I am quite surprised by the fact that the average time taken by the student to solve this question was 2:33 mins. Then, I started wondering, how many of you treat Profit and Loss as an application of percentage increase/ decrease rather than thinking of it in terms of formulae. If you follow the former, you could have solved this question much more easily.

The concept is very simple and easy to apply.
Let's start by understanding the relationship between CP, Profit %, SP as well as MP, Discount %, SP

CP, Profit %, SP

When the cost price (CP) is increased by Profit %, we will get the selling price (SP)

MP, Discount %, SP

When the marked price (MP) is reduced by Dis %, we will get the selling price (SP).

Let's try and apply this understanding in the above question.

The cost price (CP) here is 60 $ and he sold it by making a 25% profit.

So, When CP is increased by 25 %, we will get its SP i.e 60 + 25% of 60 = 60 + 15 = 75 $ or we can calculate as 125% of 60. Either way, you will end in the same SP.

Remember, the Profit here is nothing but the value increased by i.e 15$.
Also, a 40 % discount is applied on the original retail price i.e marked price (MP).

So, When MP is reduced by 40 %, we should get the same SP.

60% of MP = 75
MP = 75 * 100 /60 = 125$

Since , we are asked to find the stores profit as a percent of the original retail price (MP) i.e 15/125 * 100 = 12 %

Hence, Option B is the answer.

Thanks,
Clifin J Francis,
GMAT Quant SME

Since the answer choices are PERCENTS, the given wholesale price can be ignored.
We can plug in ANY VALUES that satisfy the relationships in the prompt.
No matter what values we plug in, \(\frac{profit}{retail-price}\) will be the same in each case.

Let the retail price = 100.
Since the CD player was sold at a 40% discount, the selling price = 60.

Since the $60 selling price enables the store to make a 25% profit on the wholesale price, the $60 selling price is 125% \(= \frac{5}{4}\) of the wholesale price:
\(60 = \frac{5}{4}W\)
\(240 = 5W\)
\(W = 48\)

Profit = (selling price) - (wholesale price) = 60-48 = 12.
Thus:
\(\frac{profit}{retail-price} = \frac{12}{100} =\) 12%


_________________

Hi all, can someone please help explain what I did wrong,

I did the Q the following way and did not get the right answer:

Set X = the % that the seller charges above WS price, so 60x = the retail price
CD is sold at 40% off the reetail price, so 0.6*60x = selling price
thus, my equation looks 60x - 0.6*60x = 15

what did I do wrong here in my equation?

profit = revenue - cost

The equation in red is incorrect because it represents the following:
retail price - selling price = profit
The profit is not equal to the difference between the retail price and the selling price.
Here, the revenue is equal to the selling price, while the cost is equal to the wholesale price.
Thus, the profit is equal to the difference between the SELLING PRICE and the WHOLESALE PRICE.

The following equation is valid:
selling price - wholesale price = profit
\(0.6(60x) - 60 = 15\)
\(36x = 75\)
\(x = \frac{75}{36} = \frac{25}{12}\)
Since you have represented the retail price as \(60x\), we get:
retail price \(= 60 * \frac{25}{12} = 125\)

What was the store's profit as a percent of the original retail price?
\(\frac{profit}{retail} * 100 = \frac{15}{125} * 100 = 12\)
_________________

Bunuel, do you have collection of such questions for practice? Could you please share their links?

Thanks,
A

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________