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Percentage problem

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by Joy Shaha » Tue Jan 24, 2017 10:38 am
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
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by Jay@ManhattanReview » Tue Jan 24, 2017 9:19 pm
Joy Shaha 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
Say the selling price be $X.

Thus, the increased profit = 20% of X = 0.2X = 9.6

=> X = 9.6/0.2 = $48.

He charged [spoiler]$48[/spoiler] per item.

Answer: D

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by [email protected] » Wed Jan 25, 2017 3:49 pm
Hi Joy Shaha,

What is the source of this question? I asked because it's poorly-worded and isn't designed in proper GMAT "style." The first sentence actually has little bearing on the prompt - other than to state that the current 'sell price' of an item leads to a profit (the 20% is a non-factor). The question essentially asks "which price, if increased by 20%, would give us an extra $9.60 in profit?"

You can TEST THE ANSWERS here, or do a bit of rounding (20% of what number is 'approximately 10') and you'll get the correct answer without too much trouble.

Final Answer: D

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by Matt@VeritasPrep » Wed Feb 01, 2017 5:54 pm
The wording is fine.

Let's say the cost to the craftsman is c. Then we've got

Normal price = c + .2c = 1.2c
Hypothetical price = 1.2c + .2*1.2c = 1.44c

We're told that hypothetical - normal = $9.60, so

1.44c - 1.2c = $9.60

.24c = $9.60

24c = $960

c = $40

That's the cost, so the normal price is 1.2c, or 1.2 * $40 = $48.
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by ceilidh.erickson » Sat Feb 04, 2017 11:28 am
Just because the question is solvable doesn't mean that the wording is "fine." I'm with Rich - wording that is confusing or misleading won't help students to do well on test day!

Joy, what is the source of this question?
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by Scott@TargetTestPrep » Wed Feb 08, 2017 6:32 pm
Joy Shaha 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
We can let r = revenue (or sale price) and c = cost.

Since profit = revenue - cost, his (original) profit would be (r - c). We are given that had the craftsman charged 20 percent more per item, his profit would have been $9.60 more. His new profit would be (1.2r - c), or (r - c + 9.6). Therefore:

1.2r - c = r - c + 9.6

0.2r = 9.6

2r = 96

r = 48

Answer: D

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by Matt@VeritasPrep » Fri Feb 17, 2017 2:10 am
ceilidh.erickson wrote:Just because the question is solvable doesn't mean that the wording is "fine." I'm with Rich - wording that is confusing or misleading won't help students to do well on test day!
What's confusing or misleading about it? Not seeing that.
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