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bmwhype2
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A fruit juice company altered its packaging from boxes measuring 30 Oct 2007, 13:17
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A fruit juice company altered its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?

A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%

M14-34

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Bunuel
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A fruit juice company altered its packaging from boxes measuring 21 Jul 2014, 00:03
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A fruit juice company altered its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?

A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%


Say the price of the box is \($x\).

The original volume was \(5 \times 10 \times 20 = 1,000\) cubic centimeters, so the price per cubic centimeter was \(\frac{x}{1,000}\);

The new volume is \(6 \times 10 \times 20 = 1,200\) cubic centimeters, so the price per cubic centimeter now is \(\frac{x}{1,200}\);

Percent decrease is \(\frac{change}{original} \times 100 = \frac{\frac{x}{1,000} - \frac{x}{1,200} }{\frac{x}{1,000} } \times 100 = \frac{1}{6} \times 100 \approx 16.67\%\).


Answer: B
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A fruit juice company altered its packaging from boxes measuring 30 Oct 2007, 21:22
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B? price has decreased by 1/6 or 16.667%.

old volume: 5*10*20=1000
new volume: 6*10*20= 1200

% change: [(old price/newvolume) - (old price/oldvolume)]/ (old price/oldvolume)

x= price

[(x/1000)-(x/1200)] / (x/1000) = [(x/1000)-(x/1200)] * (1000/x)

1 - 1000/1200 = 1 - 5/6 = 1/6
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A fruit juice company altered its packaging from boxes measuring 30 Oct 2007, 22:23
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bmwhype2
A company producing fruit juice changed its packing from boxes measuring 5*10*20 cm to boxes measuring 6*10*20 cm. If the price of a box did not change and all boxes are full of juice, by what percent did the price of the juice go down?

12%
16.67%
18.33%
20%
21.5%
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Should be B.

suppose when v = 5x10x20 = 1000 cm, the price is $1200
per cm price = $1.2

the price is $1200 if v = 6x10x20 = 1000 cm.
per cm price = $1.0

so the price is decreased by $0.2
so the % price decreased by $0.2/1.20 = 16.67%
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A fruit juice company altered its packaging from boxes measuring 17 Apr 2016, 20:38
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cubic meter old=1000ml
cubic meter new = 1200ml
assume price is 10 which is same
in order to sell 6000 ml i will sell 6 boxes, revenue =6*10=60
in order to sell 6000 ml (new box) i will sell 5 boxes , revenue=5*10=50

change=50-60/60=10/60=1/6=16.67%
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A fruit juice company altered its packaging from boxes measuring 23 Dec 2016, 16:17
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Let the price per cm3 (read cm cube) be x for the old packaging and let it be y for the new packaging.

Since the overall price remains the same, we get:
5 * 10 * 20 * x = 6 * 10 * 20 * y

canceling out 10 * 20 each side we get

5 * x = 6 * y
So y = 5x/6

Now the question asks for the reduction in price - So by how much is y less than x:
x - 5x/6 = x/6 which 1/6th
and that in percentage is 100* 1/6 = 16.67 !
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A fruit juice company altered its packaging from boxes measuring 27 Mar 2017, 09:15
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1. See that the price of the box did not change and that the volume did:

That is: PxQ=P'xQ'

-> P'/P = Q'/Q '/1200/1000 = 5/6

1/6 = 16.6%
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A fruit juice company altered its packaging from boxes measuring 07 Sep 2020, 12:59
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bmwhype2
A company producing fruit juice changed its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price of a box did not change and all boxes are full of juice, by approximately what percent did the price of the juice decrease?

A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%

M14-34
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Let the price per box = 6000 cents
Original price per volume \(= \frac{6000}{5*10*20} = 6\)
New price per volume \(= \frac{6000}{6*10*20 }= 5\)
Percent decrease \(= \frac{Difference}{Original} * 100 = \frac{6-5}{6} * 100 = \frac{1}{6} * 100 = 16.67\)

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B
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A fruit juice company altered its packaging from boxes measuring 28 Nov 2024, 19:19
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Bunuel While I agree with this solution, I have a quick question.

My mistaken solution was:

Assume the price of the bottle A as 1000, hence bottle B must have been 1200, but it is 1000 still.

So, 1200-1000/1000 * 100 = 20%.


My corrected solution:

And now when I realize the question properly & do it as per cubic cm,

Assume, 1200 as price of bottle A & hence 1.2 is the per cubic cm price; while bottle B's price w.r.t change in volume is 1.0.

Calculating: (1.2-1.0)/1.0 = 16.66%

-----------------------------------------------------------------

I'm finding it lil tricky to understand, what makes both solutions different? Can you help?


Bunuel
A fruit juice company altered its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?

A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%


Say the price of the box is \($x\).

The original volume was \(5 \times 10 \times 20 = 1,000\) cubic centimeters, so the price per cubic centimeter was \(\frac{x}{1,000}\);

The new volume is \(6 \times 10 \times 20 = 1,200\) cubic centimeters, so the price per cubic centimeter now is \(\frac{x}{1,200}\);

Percent decrease is \(\frac{change}{original} \times 100 = \frac{\frac{x}{1,000} - \frac{x}{1,200} }{\frac{x}{1,000} } \times 100 = \frac{1}{6} \times 100 \approx 16.67\%\).


Answer: B
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A fruit juice company altered its packaging from boxes measuring 29 Nov 2024, 00:12
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Sujithz001
Bunuel While I agree with this solution, I have a quick question.

My mistaken solution was:

Assume the price of the bottle A as 1000, hence bottle B must have been 1200, but it is 1000 still.

So, 1200-1000/1000 * 100 = 20%.


My corrected solution:

And now when I realize the question properly & do it as per cubic cm,

Assume, 1200 as price of bottle A & hence 1.2 is the per cubic cm price; while bottle B's price w.r.t change in volume is 1.0.

Calculating: (1.2-1.0)/1.0 = 16.66%

-----------------------------------------------------------------

I'm finding it lil tricky to understand, what makes both solutions different? Can you help?


Bunuel
A fruit juice company altered its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?

A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%


Say the price of the box is \($x\).

The original volume was \(5 \times 10 \times 20 = 1,000\) cubic centimeters, so the price per cubic centimeter was \(\frac{x}{1,000}\);

The new volume is \(6 \times 10 \times 20 = 1,200\) cubic centimeters, so the price per cubic centimeter now is \(\frac{x}{1,200}\);

Percent decrease is \(\frac{change}{original} \times 100 = \frac{\frac{x}{1,000} - \frac{x}{1,200} }{\frac{x}{1,000} } \times 100 = \frac{1}{6} \times 100 \approx 16.67\%\).


Answer: B
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Both your approaches give an incorrect 20%.

The question asks approximately what percent the price of the juice per unit of volume decreased.

If you assume that the price of both boxes is 1,000, the price per liter would be 1,000/(1 liter) and 1,000/(1.2 liters). The decrease would be:

(1,000/1 - 1,000/1.2)/(1,000/1) = 16.67%.
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