A certain manufacturer increased its gross profit on a product from 10

Question

A certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price. If the new selling price was $92.00 and the cost of the product remained the same, what was the old selling price?

A. $77.40
B. $80.00
C. $83.64
D. $87.40
E. $88.00

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Official Answer

E

Bunuel · Accepted Answer

Given:

{cost of the product} * 1.15 = $92
{cost of the product} = $80.

Therefore, the old price was $80 * 1.1 = $88.

Answer: E.

Blackbox · Answer

I am not sure I am following this question (or rather the solution that  Bunuel  responded with). Here is my thought:

Selling Price - Cost Price = Profit

Let CP = x
Old Prof =  \frac{110}{100} (x)
New Prof = \frac{115}{100} (x)

Old SP = Old Prof + CP  
=> Old SP =  \frac{110}{100} (x) + x
=> Old SP =  \frac{210}{100} (x)

Also, given

New SP = 92

New SP = New Prof + CP

=> 92 =  \frac{115}{100} (x) + x

Solving,

x =  \frac{92*100}{215}

So, the CP =  \frac{92*100}{215}

Now, plug this back into the Old SP equation above.

Old SP =  \frac{92*100}{215}  *  \frac{210}{100}

This yields a value of 89.86. Where am I going wrong? This, of course, is a loooong-winded math.

generis · Answer

Work backwards. Find cost price, which has not changed, from NEW Sell Price. Then take cost price * 1.10 to get old sell price. 1) COST PRICE? NEW Sell Price is 15% of (more than) cost price, meaning, cost price plus 15% of cost price (.15CP as a sell price won't work -- he would be selling at a price 85 percent lower than CP. Huge loss. No gross profit.) NEW Sell Price = 1.15CP = $92 $92 = 1.15CP \frac{92}{1.15} = $80 CP = $80 2) OLD Selling Price? Use CP. Old sell price was 10 percent "of" (more than) CP. Old SP = 1.10CP We now have value for CP, which is 80 Old SP is thus 1.1 * 80 = $88 Old SP = $88 ANSWER E Bunuel , given that you posted first and announced the answer, perhaps this one ought to have an official answer?

Not sure.

generis · Answer

Blackbox , I think you added in CP twice. See, e.g., partial quote of your post below. You define CP as x, but then also define old SP, it seems, as \frac{110}{100} (x) + x = 1.10 x + x Your original "100" base of the percentage of CP gets used twice, once invisibly in the second term, x. Given your direction, I think your equation should have been: \frac{10}{100} (x) + \frac{100}{100} (x) = \frac{110}{100} (x) = Old SP Old SP is not \frac{210}{100} (x), or 2.10x Old SP is 1.10x. See my solution above. Similarly, you're right on track when you define new SP as \frac{115}{100} (x). So you could just write \frac{115}{100} (x) = 92, then solve. You would get cost price of 80. I didn't run your math without the "extra" CP. But that's at least one issue. Easy mistake to make. Hope that helps.

Blackbox · Answer

Dear genxer123 , Thank you for responding. My calculations are based on my assumption Selling Price - Cost Price = Profit . Is this formula incorrect? What I understood from the prompt is that the Gross Profit was affected as per this condition -- "... increased its gross profit on a product from 10 percent of the cost of the product ..." . What I do not understand is why that condition is equated to Selling Price. For e.g., NEW Sell Price = 1.15CP = $92. I am clearly confused

generis · Answer

Dear Blackbox , Of course the formula is correct! I've seen your posts, including the recent one on that horrible problem about a gasoline price increase (and a guy, Ron, who could afford part of the increase, such that we had to calculate by what percentage he must decrease consumption). You nailed it. I solved it. Barely. In FOUR minutes. I got stuck. So I think you are just a little stuck on this one. You are not calculating profit correctly in the equation "Selling Price - Cost Price = Profit"! You are forgetting to subtract 100 percent of the cost price from the equation! I would PM you this whole thing, but math symbols and formulas are not translated any longer on PMs. Incorrect figures are in red. Strike through will not work on fractions. Correct figures are in blue. I beg you: at some point, use multipliers for percentages?

Selling Price - Cost Price = Profit Let CP = x Old Prof = \frac{110}{100} (x) New Prof = \frac{115}{100} (x) Old Prof = \frac{110}{100} (x) - 1x Old Prof = \frac{110}{100} (x) - \frac{100}{100} (x) = \frac{10}{100} (x) New Prof = \frac{115}{100} (x) - 1x New Prof = \frac{115}{100}(x) - \frac{100}{100}(x) = \frac{15}{100}(x) Old SP = Old Prof + CP => Old SP = \frac{110}{100} (x) + x => Old SP = \frac{210}{100} (x) + x Old SP = Old Prof + CP => Old SP= \frac{10}{100} (x) + x => Old SP \frac{10}{100} (x) + \frac{100}{100} (x) => Old SP = \frac{110}{100} (x) Also, given New SP = 92 New SP = New Prof + CP => 92 = \frac{115}{100} (x) + x => 92 = \frac{15}{100} (x) + x =>92 = \frac{115}{100} (x) Solving, REPEAT THE EQUATION FROM ABOVE 92 = \frac{115}{100} (x) x = \frac{92*115}{100} x = 92 * \frac{100}{115} x = 80 So, the CP = \frac{92*100}{215} So, the CP = 80 Now, plug this back into the Old SP equation above. Old SP = \frac{92*100}{215} * \frac{210}{100} Old SP = (92 * \frac{100}{115} ) * \frac{110}{100} = $88 I so hope that helps. Your formula was fine. (Hard, but fine.) I just redid your math, and voila, the answer!

Blackbox · Answer

Oh.My.God. I can totally see where I went wrong. I feel so stupid right now

. I guess that's what you get when you do 60 Verbal and Math questions back to back. Thank you, genxer123 . I really appreciate your taking time to lay the math out.

Edg_Tbr · Answer

hello  Bunuel , do you have a simple methodology to solve quickly the fraction 92/1.15=9200/115. 
The objective it is not to do it by iteration.
Thanks

Vesper2018 · Answer

Convert 1.15 to fraction: 1.15 = 1 15/100 or 1 3/20 or 23/20 
 Then do division of fractions: 92/1 divided by 23/20 = 80

Abhishek009 · Answer

Screenshot 2024-03-25 120813.png Cost remain the same 100 only Selling price changes with change in profit. Thus old selling price will be : \frac{92}{115}*110 = 88 , Answer will be (E)

Nalapatricia · Answer

Hello, Bunuel or bb , could you change the source of this questions to Gmat focus prep? this question appears on Mock number 5. regards, Nalapatricia. https://gmatclub.com/forum/download/file.php?id=82995 GMAT-Club-Forum-mt1ovz0o.jpeg

Bunuel · Answer

_______________ Done. Thank you! GMAT-Club-Forum-odlli7tr.jpeg

MyNameisFritz · Answer

S=selling price
C=cost

92-C=(15/100)C
92=(115/100)C
C=80

The old profit from the old selling price was 1/10 of Cost, therefore:
S-80=(1/10)C
S-80=8
S=88

Answer E.

A certain manufacturer increased its gross profit on a product from 10

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