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A craftsman sold his identical handcrafted items at a profit of 20 per

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EgmatQuantExpert
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A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   22 Jan 2017, 01:14
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A craftsman sold his identical handcrafted items at a profit of 20 percent. Had he charged 20 percent more per item, his profit per item would have been $9.6 more. What price did he charge, in dollars, for each item?

    A. 24
    B. 28.8
    C. 40
    D. 48
    E. 57.6

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D
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   Updated on: 27 Jan 2017, 23:50
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The official solution has been posted. Looking forward to a healthy discussion..:)

Originally posted by EgmatQuantExpert on 22 Jan 2017, 01:16.
Last edited by EgmatQuantExpert on 27 Jan 2017, 23:50, edited 1 time in total.
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rohit8865
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   22 Jan 2017, 12:04
EgmatQuantExpert wrote:
Q.)
A craftsman sold his identical handcrafted items at a profit of 20 percent. Had he charged 20 percent more per item, his profit per item would have been $9.6 more. What price did he charge, in dollars, for each item?

    A. 24
    B. 28.8
    C. 40
    D. 48
    E. 57.6

Thanks,
Saquib
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Let x be CP of item
then profit of 20% over already increased 20% of Cost price = (6/5)^2*x
profit @ only 20% increase = (6/5)*x-x = 0.2x
per stem
(6/5)^2*x = 0.2x+9.2
6x/25=9.6
x=40
thus initially he charge 20% profit over $40
(6/5)*40 = $48

Ans D
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   27 Jan 2017, 23:49
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Hey,

PFB the official solution.


Given:

    • Let the Cost Price of each item be\(C\) dollars and the selling price be \(S\)dollars
    • If Selling Price is \(20\)% more, profit per item is $\(9.6\) more

To find:

    • \(S =\)?


Approach:

    1. To find the value of S, we need to draft an equation in terms of S.
    2. We’re given the relation between Old Profit (when the selling price is S) and the New Profit (when the selling price is 20% greater than S). We’ll use this relation to draft an equation in terms of S.

Working Out:

    • New Selling Price = \(S + 20% * S = S + 0.2S = 1.2S\)
    • New Profit = (Old Profit) + $\(9.6\)
      o New profit = New SP – CP \(= 1.2S – C\)
      o Old profit = Old SP – CP\(= S - C\)
    • So, \((1.2S – C) = (S – C) + 9.6\)• \(0.2S = 9.6\)
    • \(S = \frac{9.6}{0.2}\)
    • \(S = 48\)

Looking at the answer choices, we see that the correct answer is Option D

Thanks,
Saquib
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   28 Jan 2017, 00:40
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The price after 20% percent profit = 1.2x

Another 20% profit means 1.2x/5 = 0.24x = 9.6

x = 40.

So the original price = 40 + 40/5 = 48.
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   26 Mar 2019, 02:23
Hello Saqib,

Its not clear from the stem that 20% more on the Selling price of 1.2C (which will make the selling price 1.44C), or 20% extra of CP on the selling price (which will make the selling price 1.2C+.2C = 1.4C)

Only thing mentioned is : Had he charged 20 percent more per item

Kindly explain, to understand better.
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   30 Mar 2019, 03:13
EgmatQuantExpert wrote:
Hey,

PFB the official solution.


Given:

    • Let the Cost Price of each item be\(C\) dollars and the selling price be \(S\)dollars
    • If Selling Price is \(20\)% more, profit per item is $\(9.6\) more

To find:

    • \(S =\)?


Approach:

    1. To find the value of S, we need to draft an equation in terms of S.
    2. We’re given the relation between Old Profit (when the selling price is S) and the New Profit (when the selling price is 20% greater than S). We’ll use this relation to draft an equation in terms of S.

Working Out:

    • New Selling Price = \(S + 20% * S = S + 0.2S = 1.2S\)
    • New Profit = (Old Profit) + $\(9.6\)
      o New profit = New SP – CP \(= 1.2S – C\)
      o Old profit = Old SP – CP\(= S - C\)
    • So, \((1.2S – C) = (S – C) + 9.6\)• \(0.2S = 9.6\)
    • \(S = \frac{9.6}{0.2}\)
    • \(S = 48\)

Looking at the answer choices, we see that the correct answer is Option D



Could you please explain why
So, \((1.2S – C) = (S – C) + 9.6\)• \(0.2S = 9.6\)

I just couldnt get it.
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   30 Apr 2020, 03:37
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EgmatQuantExpert wrote:
Q.)
A craftsman sold his identical handcrafted items at a profit of 20 percent. Had he charged 20 percent more per item, his profit per item would have been $9.6 more. What price did he charge, in dollars, for each item?

[list]A. 24
B. 28.8
C. 40
D. 48
E. 57.6


Let x = the current selling price of the item. Thus, adding 20% more would make the new selling price 1.2x, and the extra 20%, or 0.2x, is equal to $9.60. Thus, we have

0.2x = 9.6

x = 48

Answer: D
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   30 Apr 2020, 09:09
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A simpler answer would be:
Let x be the selling price
20% more is 1.2 x

Then Equate according to the question

1.2x-x=9.6

X=9.6/.2 which is 48 ans

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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink] New post   01 May 2023, 10:07
EgmatQuantExpert

I agree with rocky620 that the question is ambiguous. "20% more" could mean 20% more than the original 20% (i.e. 40%), or 20% on top of the original 20% (6/5*6/5). However ScottTargetTestPrep clarifies that this doesn't really matter, since the core of the question is basically "20% of the sale price is $9.6, so what is the sale price?" at which point you can still get to the official answer D
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Re: A craftsman sold his identical handcrafted items at a profit of 20 per [#permalink]
01 May 2023, 10:07
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