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

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Manager
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A manufacturer makes umbrellas at the cost of c dollars pe [#permalink]  27 Feb 2013, 03:16
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Question Stats:

60% (03:52) correct 40% (03:12) wrong based on 87 sessions
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, 04:53, 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, 03:27
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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 = $$\frac{x(2c-r)}{(b-r)}$$

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Re: A manufacturer makes umbrellas at the cost of c dollars pe [#permalink]  28 Feb 2013, 02:33
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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
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Re: A manufacturer makes umbrellas at the cost of c dollars pe [#permalink]  11 Jan 2014, 07:36
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?

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

Could anybody try smart numbers on this one? I'm having a tough time coming up with the solution

Thanks!
Cheers!
J
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Re: A manufacturer makes umbrellas at the cost of c dollars pe [#permalink]  13 Sep 2014, 15:44
leekay wrote:
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

Good approach, but still I don´t understand how to choose between B and C.
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Re: A manufacturer makes umbrellas at the cost of c dollars pe   [#permalink] 13 Sep 2014, 15:44
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