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A retail store that sells only shoes and accessories found

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A retail store that sells only shoes and accessories found [#permalink] New post 04 Mar 2012, 13:25
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A
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D
E

Difficulty:

  5% (low)

Question Stats:

88% (02:31) correct 12% (01:36) wrong based on 101 sessions
A retail store that sells only shoes and accessories found that its revenues last month from those two categories could be expressed in the ratio x : y, respectively. If last month's total revenues were $4,000, what was the difference between revenues from shoes and revenues from accessories?

A. \(\frac{x}{x+y}\)

B. \(\frac{y}{x+y}\)

C. \($4,000 * \frac{x}{y}\)

D. \($4,000*\frac{x}{x+y}\)

E. \(\frac{$4,000*(x-y)}{x+y}\)


Any idea how to get to answer E?
This is how I am trying to solve

Let the revenue from shoes be \(5x\)and revenue from accessories be \(5y.\)

Total revenue = \(5x + 5y = 4000\)

Revenue from shoes = \(\frac{5x}{5x+5y}\)
Revenue from accessories = \(\frac{5y}{5x+5y}\)

Difference in revenues = \(\frac{5x}{5x+ 5y} - \frac{5y}{5x - 5y}\)

But this won't give me the right answer. Any thoughts why guys?
[Reveal] Spoiler: OA

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Re: Shoes & Accessories [#permalink] New post 04 Mar 2012, 14:03
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A retail store that sells only shoes and accessories found that its revenues last month from those two categories could be expressed in the ratio x : y, respectively. If last month's total revenues were $4,000, what was the difference between revenues from shoes and revenues from accessories?

A. \(\frac{x}{x+y}\)

B. \(\frac{y}{x+y}\)

C. \($4,000 * \frac{x}{y}\)

D. \($4,000*\frac{x}{x+y}\)

E. \(\frac{$4,000*(x-y)}{x+y}\)

The revenues from shoes and accessories were in the ratio x:y;

Share of revenues from shoes in total revenues is \(\frac{x}{x+y}\), hence revenues from shoes is \(4,000*\frac{x}{x+y}\);
Share of revenues from accessories in total revenues is \(\frac{y}{x+y}\), hence revenues from accessories is \(4,000*\frac{x}{x+y}\);

Difference: \(4,000*\frac{x}{x+y}-4,000*\frac{y}{x+y}=\frac{4,000(x-y)}{x+y}\).

Answer: E.
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Re: A retail store that sells only shoes and accessories found [#permalink] New post 05 Mar 2013, 10:18
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enigma123 wrote:
A retail store that sells only shoes and accessories found that its revenues last month from those two categories could be expressed in the ratio x : y, respectively. If last month's total revenues were $4,000, what was the difference between revenues from shoes and revenues from accessories?

A. \(\frac{x}{x+y}\)

B. \(\frac{y}{x+y}\)

C. \($4,000 * \frac{x}{y}\)

D. \($4,000*\frac{x}{x+y}\)

E. \(\frac{$4,000*(x-y)}{x+y}\)


Nothing extra to add. But in case any one wants to gain some extra seconds, put x=y=1, i.e. they both have equal revenue. Thus their difference would be 0. Only option E satisfies that condition.

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Re: A retail store that sells only shoes and accessories found [#permalink] New post 12 Jun 2013, 07:27
Hi Bunuel
Please explain

Share of revenues from shoes in total revenues is , hence revenues from shoes is ;4000*x/x+y
Share of revenues from accessories in total revenues is , hence revenues from accessories is ;4000*y/x+y

Rgds
Prasannajeet
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Re: A retail store that sells only shoes and accessories found [#permalink] New post 12 Jun 2013, 08:12
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prasannajeet wrote:
Hi Bunuel
Please explain

Share of revenues from shoes in total revenues is , hence revenues from shoes is ;4000*x/x+y
Share of revenues from accessories in total revenues is , hence revenues from accessories is ;4000*y/x+y

Rgds
Prasannajeet


Say x=1 and y=3. Total of 1+3=4 parts:
Share of shoes = 1/(1+3)=1/4 --> revenue 1/4*4000=1000.
Share of accessories = 3/(1+3) = 3/4 --> revenue 3/4*4000=3000.

Difference = 2000.
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COLLECTION OF QUESTIONS:
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Re: A retail store that sells only shoes and accessories found [#permalink] New post 13 Jun 2013, 02:04
Hi Bunuel

Thanx and +1 Kudos to you...
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Re: A retail store that sells only shoes and accessories found [#permalink] New post 19 Jan 2015, 04:46
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Re: A retail store that sells only shoes and accessories found   [#permalink] 19 Jan 2015, 04:46
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