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

Question

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

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rohit8865 · Answer

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

EgmatQuantExpert · Answer

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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RMD007 · Answer

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.

rocky620 · Answer

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.

khiemchii · Answer

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

I just couldnt get it.

ScottTargetTestPrep · Answer

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

Arssalan8 · Answer

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

Posted from my mobile device

gmattyfatty · Answer

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

mithxrx · Answer

Very confused on why we can do Profit??Increase=(1.2p???c)???(p???c)=1.2p???p=0.2p and set 0.2p=9...Why does p-c have the 20% profit baked in?

ManishaPrepMinds · Answer

Your confusion is valid. Profit is usually defined over cost, but here we are comparing profits based on selling prices (P, 1.2P).
This works only if you realize that P already includes the 20% markup on cost.
So yes, P – C = 0.2C, and you can directly work with selling prices only if you’re clear on that assumption. Here, P already contains the 20% profit information

Let C = Cost price
Let P = Selling price
Given: Profit of 20%, so
P = 1.2C
So, P – C = 0.2C → this is your profit per item.

He increased the price by 20%
New price = 1.2P
New profit = 1.2P – C
Increase in profit:
= (1.2P – C) – (P – C)
= 1.2P – C – P + C
= 0.2P

0.2P = 9.6 
P = 48

Much easier approach,

Original Selling Price (SP) = 1.2C
New SP (with 20% increase) = 1.2C × 1.2 = 1.44C
Profit Increase = 1.44C – C – (1.2C – C)
= 0.44C – 0.2C = 0.24C
so:
0.24C = 9.6 
C = 40
SP = 1.2C = 1.2 × 40 = 48

socialsloth · Answer

Quite ambigous, 20% more per item sounds like + 20% of Cost price.

Admins  is there some way to tag/report so that applicants need not feel confused?

Bunuel · Answer

Use Report button: https://gmatclub.com/forum/download/file.php?id=86603 GMAT-Club-Forum-wft5y1qz.png

Dereno · Answer

Let the initial cost price be 100c

The selling price at a profit of 20% will give us 120c

100c * (20/100) = 20c.

S.P = 100c + 20c = 120c

If the price is increased by another 20% , we get

120c *   = 144c

Thus the increase = 144c - 100c = 44c

This profit would have been $9.6 more.

44c = 20c + $9.6

24c = $9.6

c =$9.6/24

c = $0.4

Cost price = 100c =100 * 0.4 = $40

Selling price = 120c = 120 * 0.4 =  $48

Option D

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

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

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