A manufacturer makes umbrellas at the cost of c dollars pe

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A manufacturer makes umbrellas at the cost of c dollars pe [#permalink]

27 Feb 2013, 04:16

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A manufacturer makes umbrellas at the cost of c dollars per umbrella, and sells them at the retail price of r dollars each. How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?

A. \frac{b(2c-r)}{(x-r)}

B. \frac{2x(c-r)}{(b-r)}

C. \frac{x(2c-r)}{(b-r)}

D. \frac{2b(c-r)}{(x-r)}

E. \frac{2(xc-r)}{(x-r)}

[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Feb 2013, 05:53, edited 1 time in total.

Edited the question.

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Re: A manufacturer makes umbrellas at the cost of c dollars pe [#permalink]

27 Feb 2013, 04:27

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emmak wrote:

A manufacturer makes umbrellas at the cost of c dollars per umbrella, and sells them at the retail price of r dollars each. How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit on its lot of x total umbrellas?

\frac{b(2c-r)}{(x-r)}

\frac{2x(c-r)}{(b-r)}

\frac{x(2c-r)}{(b-r)}

\frac{2b(c-r)}{(x-r)}

\frac{2(xc-r)}{(x-r)}

Let "N" be the required answer.,

(x - N)r + Nb = 2xc

xr - Nr + Nb = 2xc

N(b - r) = x(2c - r)

N = \frac{x(2c-r)}{(b-r)}

Answer is C
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Re: A manufacturer makes umbrellas at the cost of c dollars pe [#permalink]

28 Feb 2013, 03:33

process of elimination + intuition

x and r are not of the same nature (cost in dollar and total umbrellas) => eliminate A,D,E
now, with some intuition, if retail price is less than cost, B would be negative => eliminate B
Answer is C

Re: A manufacturer makes umbrellas at the cost of c dollars pe [#permalink] 28 Feb 2013, 03:33

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A manufacturer makes umbrellas at the cost of c dollars pe

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A manufacturer makes umbrellas at the cost of c dollars pe

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