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

Question

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

BillyZ · Accepted Answer

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%.

mohshu · Answer

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

quantumliner · Answer

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%

Answer is B. 20%

SeregaP · Answer

(3-C)/C=0,2 C=2,5
(3-C)/C=0,5 C=2
(2,5-2)/2,5=-0,2

Answer by 20% (B)

IdiomSavant · Answer

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%

Cez005 · Answer

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

Kudos if you agree!

stonecold · Answer

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

SamBoyle · Answer

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%

TimeTraveller · Answer

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.

anirchat · Answer

Very nice twisty question, easy but GMAT standard.

(1- 2/2.5) X 100 % = 20 %

OJA · Answer

If the profit margin was 20%, then the cost of the drink is $2.5.

Keeping the SP as constant, and profit margin to be 50%, the new cost of the drink turns out to be $2.

After that, it is simply unitary method.

If $2.5 corresponds to 1L, then $2 will be (1/2.5) * 2 = 800 ml.

To calculate the % reduction = 200ml/1000ml = 20%.

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

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