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# Word Problem - A craftsman sold his identical handcrafted items at a p

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2812
Word Problem - A craftsman sold his identical handcrafted items at a p  [#permalink]

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22 Jan 2017, 01:14
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

50% (02:13) correct 50% (02:25) wrong based on 88 sessions

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 Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts _________________ e-GMAT Representative Joined: 04 Jan 2015 Posts: 2812 Word Problem - A craftsman sold his identical handcrafted items at a p [#permalink] ### Show Tags Updated on: 27 Jan 2017, 23:50 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. Director Joined: 05 Mar 2015 Posts: 999 Re: Word Problem - A craftsman sold his identical handcrafted items at a p [#permalink] ### Show Tags 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
Quant Expert
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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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2812
Re: Word Problem - A craftsman sold his identical handcrafted items at a p  [#permalink]

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27 Jan 2017, 23:49
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
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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Re: Word Problem - A craftsman sold his identical handcrafted items at a p  [#permalink]

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28 Jan 2017, 00:40
1
1
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.
Intern
Joined: 10 Nov 2018
Posts: 12
Re: Word Problem - A craftsman sold his identical handcrafted items at a p  [#permalink]

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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.
Intern
Joined: 19 Nov 2016
Posts: 9
Re: Word Problem - A craftsman sold his identical handcrafted items at a p  [#permalink]

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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

So, $$(1.2S – C) = (S – C) + 9.6$$• $$0.2S = 9.6$$

I just couldnt get it.
Re: Word Problem - A craftsman sold his identical handcrafted items at a p   [#permalink] 30 Mar 2019, 03:13
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