Profit Percent and Loss Percent

Brent, I'm with you - I'm getting hooked on trying to unravel these beautifully inscrutable questions.

A Google search for "loss percent" turned up this brainfrying resource, which I'm applying here as follows:

c = cost of the article
x = price at which the article is sold
2x = double that
loss percent = how much we'd LOSE if we sold the article for x = (c - x)/c * 100
profit percent = how much we'll GAIN by selling the article for 2x = (2x - c)/c * 100

Since the percentages are the same, we have

100 * (c - x)/c = 100 * (2x - c)/c
(c - x) = (2x - c)
2c = 3x
x = (2/3)c

The loss percent is 100 * (x - c)/c or 100 * (1/3)c / c or -33.3...%. Since our definition seems to encourage us to take the absolute value of this percentage, |-33.3...%| yields the same result as our profit percent, which is 100 * (2x - c)/c = 100 * (1/3)c/c or 33.3...%.

Warning, readers: I have no clue if my interpretation is correct.

Brent@GMATPrepNow wrote:Ahhhhh!
BTW, I loved the Lewis Carroll reference in your original response

So, I guess the answer is "none of the above," since 33 1/3% is not among the answer choices

Cheers,
Brent

I took that out in the interests of diplomacy - maybe the guy who wrote this question will one day be my student, or my boss, or whatever ... and maybe he doesn't care for Lewis Carroll.

I think 33.33% is supposed to be the question's way of writing 33.3...% (After all, Humpty Dumpty would tell us that the value of a number means what we want it to mean, neither more, nor less!)

The intent of the problem seems to be as follows:

Because of a clerical error, a shirt was marked with a selling price that was x% less than the cost price of the shirt. After the error was discovered, the selling price of the shirt was doubled, with the result that the corrected selling price was x% greater than the cost price of the shirt. What is the value of x?

12.5 %
25%
33 1/3%
40%
50%

We can PLUG IN THE ANSWERS, which represent the value of x.
When the correct answer choice is plugged in, the corrected selling price will be DOUBLE the incorrect selling price.
Let the cost price = 100.

Answer choice D: 40%
Incorrect selling price = 100 - (40% of 100) = 60.
Corrected selling price = 100 + (40% of 100) = 140.
Here, the corrected selling price (140) is MORE THAN DOUBLE the incorrect selling price (60).
Eliminate D.

Answer choice B: 25%
Incorrect selling price = 100 - (25% of 100) = 75.
Corrected selling price = 100 + (25% of 100) = 125.
Here, the corrected selling price (125) is LESS THAN DOUBLE the incorrect selling price (75).
Eliminate B.

Since 40% yields a corrected selling price that is MORE than double the incorrect selling price, and 25% yields a corrected selling price that is LESS than double the incorrect selling price, the required percentage must be BETWEEN 25% and 40%.

The correct answer is C.

Answer choice C: 33 1/3%
Since 33 1/3% = 1/3, let the cost price = $30.
Incorrect selling price = 30 - (1/3 of 30) = 20.
Corrected selling price = 30 + (1/3 of 30) = 40.
Success!
The corrected selling price (40) is double the incorrect selling price (20).

Yup, Mitch, I think you've got it! The confusing thing about "loss percent" in that definition I found is that it's treated as a positive value even though it isn't actually positive.

For anyone out there who wants more practice, the spirit of this problem reminds me of this (hellacious) problem from an old American High School Math Exam:

An article costing C dollars is sold for $100 at a loss of x percent of the selling price. It is then resold at a profit of x percent of the new selling price S. If the difference between S and C is $1.11..., then x is

A:: Undetermined
B:: 80/9
C:: 10
D:: 95/9
E:: 100/9

If the selling price of an article is doubled, then it's loss percent is converted into equal profit percent. The loss percent on the article is

A) 26.66%
B) 33%
C) 33.33%
D) 34%
Let , L=10
(L=CP-SP)
10=CP-SP......(1)
A/Q, IF SP is DOUBLED then Loss becomes profit.
So, L=P=10
(P=SP - CP)
10=2SP-CP......(2)
EQUATING 1&2
CP-SP=2SP-CP
2CP=3SP
CP:SP = 3:2
So,
L= 3-2=1
L% = L/CP ×100
L% = 1/3 × 100 =33.33%

coolhabhi wrote:If the selling price of an article is doubled, then it's loss percent is converted into equal profit percent. The loss percent on the article is

A) 26.66%
B) 33%
C) 33.33%
D) 34%

Loss percent is defined as (loss/cost price) × 100% and profit percent is defined as (profit/cost price) x 100%. We can assume that if the article is sold at its original selling price, a loss will incur (even though the problem didn’t clearly mention it). However, if the article is sold at double of its original selling price, a profit will incur. Thus let’s let s = the original selling price and c = the cost price. Therefore, the loss = c - s if the article is sold at price s and the profit = 2s - c if the article is sold at price 2s. Since we are given that the loss percent = the profit percent, We can create the following equation:

(c - s)/c x 100% = (2s - c)/c x 100%

(c - s)/c = (2s - c)/c

c - s = 2s - c

2c = 3s

s = 2c/3

Therefore, substituting s with 2c/3, the loss percent is:

(c - 2c/3)/c x 100% = (c/3)/c x 100% = 1/3 x 100% = 33.33%

Answer: C

Matt@VeritasPrep wrote:Yup, Mitch, I think you've got it! The confusing thing about "loss percent" in that definition I found is that it's treated as a positive value even though it isn't actually positive.

For anyone out there who wants more practice, the spirit of this problem reminds me of this (hellacious) problem from an old American High School Math Exam:

An article costing C dollars is sold for $100 at a loss of x percent of the selling price. It is then resold at a profit of x percent of the new selling price S. If the difference between S and C is $1.11..., then x is

A:: Undetermined
B:: 80/9
C:: 10
D:: 95/9
E:: 100/9

The first statement rendered to make X positive:

C-100 = X

The second statement:

S-100 = S*X/100

The third statement:

S - C =1.11 repeating =10/9 > S = (9C+10)/9

On a hunch, try X = 10 as a potential solution and see if everything foots:

Therefore C = 110 from the first statement

S = (990 + 10)/9 = 1000/9 from the third statement

Does (1000/9) - 100 = (1000/9) * 10/100 from the second statement ?

(1000/9) - 100 = (1000-900)/9 = 100/9

(1000/9)*(10/100) = (1000/9)*(1/10) = 100/9 > success [spoiler]1X=10, C[/spoiler]