A Craftsman Sold his Identical Items a t a Profit of 20 Percent GMAT Problem Solving

Question: A craftsman sold his identical items a t 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?

1. 24
2. 28.8
3. 40
4. 48
5. 57.6

Answer:
Solution with Explanation:
Approach Solution (1):

Let x be CP of item
Then profit of 20% over already increased 20% of cost price = \((\frac{6}{5})^2*x\)
Profit @ only 20% increase = \((\frac{6}{5})*x-x = 0.2x\)
Per stem
\((\frac{6}{5})^2*x = 0.2x + 9.2\)
\(\frac{6x}{25} = 9.6\)
x=40

Thus initially he charge 20% profit over $40

\((\frac{6}{5})*40 = $48\)

Correct Option: D

Approach Solution (2):

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
New selling price = S + 20
New profit = (Old profit) + 9.6
New profit = New SP – CP = 1.2S – C
Old profit = Old SP – CP = S – C
So, (1.2S – C) = (S – C) + 9.6
0.2 S = 9.6
S = 48

Correct Option: D

Approach Solution (3):

A simpler answer would be:
Let x be the selling price
20% more is 1.2x
Then equate according to the question:
1.2x – x = 9.6
x = \(\frac{9.6}{0.2} = 48\)

Correct Option: D

“A craftsman sold his identical items a t 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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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