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# A soft drink company currently sells its most popular product in one-l

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Math Expert
Joined: 02 Sep 2009
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A soft drink company currently sells its most popular product in one-l  [#permalink]

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07 Mar 2017, 01:05
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Difficulty:

75% (hard)

Question Stats:

60% (02:30) correct 40% (03:05) wrong based on 233 sessions

A soft drink company currently sells its most popular product in one-liter containers for $3, yielding a 20% profit margin on the cost. If cost is proportional to volume, by what percent should the company reduce the volume of the container to yield a 50% profit margin on the cost, assuming the selling price remains the same? A. 10% B. 20% C. 25% D. 33% E. 50% _________________ Director Joined: 21 Mar 2016 Posts: 521 Re: A soft drink company currently sells its most popular product in one-l [#permalink] ### Show Tags 07 Mar 2017, 04:00 2 since the profit % is 20, the cost price is 2.5$.
cost of 1 litre is 2.5$. since selling price remains same,, inorder to get 50% margin the cost price should be 2$.

hence reduce the volume by 20%

ans B
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Re: A soft drink company currently sells its most popular product in one-l  [#permalink]

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07 Mar 2017, 12:09
1
Let the cost of one-liter container = $100x After 20% profit the Selling Price of the one-liter container =$120x
Given Selling Price of the one-liter container = $3 Finding value of X => 120x= 3 => x=1/40 therefore cost of one-liter container =$100x = 100 * 1/40 = $2.5 Now to get 50% profit, the selling price would be$150x, if the initial cost is 100x
Given: Selling Price remains the same, therefore, 150x=3 => x=1/50
Cost Price = $100x = 100* 1/50 =$2

therefore the reduction in volume = (2.5 - 2) *100 /2.5 = 20%

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Re: A soft drink company currently sells its most popular product in one-l  [#permalink]

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07 Mar 2017, 13:58
(3-C)/C=0,2 C=2,5
(3-C)/C=0,5 C=2
(2,5-2)/2,5=-0,2

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Joined: 14 Sep 2016
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Concentration: Finance, Economics
Re: A soft drink company currently sells its most popular product in one-l  [#permalink]

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07 Mar 2017, 14:02
Bunuel wrote:
A soft drink company currently sells its most popular product in one-liter containers for $3, yielding a 20% profit margin on the cost. If cost is proportional to volume, by what percent should the company reduce the volume of the container to yield a 50% profit margin on the cost, assuming the selling price remains the same? A. 10% B. 20% C. 25% D. 33% E. 50% A little confusing because a profit margin is never calculated as a percent of cost rather than percent of revenue... Old Revenue 3 Expense 2.5 80.00% Gross Profit 0.5 20.00% New Revenue 3 Expense 2 50.00% Gross Profit 1 50.00% 0.5/2.5 = 20% Senior SC Moderator Joined: 14 Nov 2016 Posts: 1324 Location: Malaysia A soft drink company currently sells its most popular product in one-l [#permalink] ### Show Tags 21 Mar 2017, 04:12 4 Bunuel wrote: A soft drink company currently sells its most popular product in one-liter containers for$3, yielding a 20% profit margin on the cost. If cost is proportional to volume, by what percent should the company reduce the volume of the container to yield a 50% profit margin on the cost, assuming the selling price remains the same?

A. 10%
B. 20%
C. 25%
D. 33%
E. 50%

OFFICIAL SOLUTION

Begin by finding the cost of the 1-liter container: 1.2c = 3, and c = 2.5. Next, let’s figure out how much the product cost should be to create the 50% profit margin: 1.5x = 3, and x = 2. Since cost is proportional to volume, the percent change in cost is the same as the percent change in volume: $$\frac{(2.5 - 2.0)}{2.5} = \frac{0.5}{2.5}$$= 20%.
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Re: A soft drink company currently sells its most popular product in one-l  [#permalink]

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04 Apr 2017, 19:40
1L=3
Sale price = 3
Cost price = 3*(5/6) = 2.50
Cost price for profit to equal 50% of cost price = 2
2.50*0.8=2. A 20% reduction.
If volume is proportional to cost then volume must also be reduced by 20%. B

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Re: A soft drink company currently sells its most popular product in one-l  [#permalink]

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16 Jun 2017, 18:18
Original CP => 30/1.2 => 2.5

New CP => 3/1.5 => 2

Percent reduction in CP => 0.5/2.5 * 100 => 20

Hence percentage reduction in SP would be 20 as well.

Hence B
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A soft drink company currently sells its most popular product in one-l  [#permalink]

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08 Jul 2017, 11:22
IdiomSavant wrote:
Bunuel wrote:
A soft drink company currently sells its most popular product in one-liter containers for $3, yielding a 20% profit margin on the cost. If cost is proportional to volume, by what percent should the company reduce the volume of the container to yield a 50% profit margin on the cost, assuming the selling price remains the same? A. 10% B. 20% C. 25% D. 33% E. 50% A little confusing because a profit margin is never calculated as a percent of cost rather than percent of revenue... Old Revenue 3 Expense 2.5 80.00% Gross Profit 0.5 20.00% New Revenue 3 Expense 2 50.00% Gross Profit 1 50.00% 0.5/2.5 = 20% Exactly, the wording is bad but probably intentionally so. A 20% profit margin on the cost means X * 1.2 = 3. So 3/1.2 is$2.5, which is the cost. If 2.5 is the cost what do we need to reduce it buy to get to 50%? well X *1.5 = 3 and 3/1.5 = 2. Therefore we reduced the volume from 2.5 to 2 or 0.5 /2.5 or 20%
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Re: A soft drink company currently sells its most popular product in one-l  [#permalink]

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08 Jul 2017, 18:28
SP = $3, P = 0.2, so CP =$3/1.2 = $2.5. For P to be 0.5, CP =$3/1.5 = \$2.

Since the volume is proportional to the cost, the volume should be reduced by (1 - 2/2.5) = 20%. Ans - B.
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Re: A soft drink company currently sells its most popular product in one-l  [#permalink]

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18 Aug 2018, 04:21
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Re: A soft drink company currently sells its most popular product in one-l &nbs [#permalink] 18 Aug 2018, 04:21
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