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The value of a precious stone is directly proportional to the cube of

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The value of a precious stone is directly proportional to the cube of [#permalink]

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New post 19 Nov 2017, 11:47
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A
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C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (01:25) correct 37% (00:59) wrong based on 38 sessions

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The value of a precious stone is directly proportional to the cube of its weight. If a big stone broke into three parts in the ratio 1:4:5, what was the percentage drop in the value of the stone?

A. 10%
B. 40%
C. 71%
D. 81%
E. 93%

source: Experts Global
[Reveal] Spoiler: OA

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The value of a precious stone is directly proportional to the cube of [#permalink]

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New post 19 Nov 2017, 12:24
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pushpitkc wrote:
The value of a precious stone is directly proportional to the cube of its weight. If a big stone broke into three parts in the ratio 1:4:5, what was the percentage drop in the value of the stone?

A. 10%
B. 40%
C. 71%
D. 81%
E. 93%

source: Experts Global


Let the original weight of the stone be \(10\) units

so original price \(P=10^3k=1000k\), where \(k\) is any constant

as the stone broke in the ratio \(1:4:5\), so the weight of the three stones will be \(1\), \(4\) & \(5\). Revised price will be

\(P_1=1^3k=k\)

\(P_2=4^3k=64k\)

\(P_3=5^3k=125K\)

So Total new price \(= k+64k+125k=190k\)

Hence reduction in price \(= 1000k-190k=810k\)

Reduction % \(= \frac{810k}{1000k}*100=81\)%

Option D

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Re: The value of a precious stone is directly proportional to the cube of [#permalink]

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New post 19 Nov 2017, 12:48
Let's assume initial weight of the precious stone as 10 (1+4+5) and original value as 1000.
As the stone gets broken into 3 parts in the ratio of 1: 4: 5, therefore, the weights of the pieces will be in the same ratio.
Let the value of these 3 pieces be x, y, and z respectively, hence, we get that:
\(\frac{1000}{x}=\frac{10^3}{1^3}\), or, x=1.
Similarly, \(\frac{1000}{y}=\frac{10^3}{4^3}\), giving y=64, and
\(\frac{1000}{z}=\frac{10^3}{5^3}\), giving z=125

Therefore, the new value of the stone will be x+y+z, or, 1+64+125 = 190.

%age change = \(\frac{Old Value - New Value}{Old Value}\)*100

%age change = \(\frac{1000-190}{1000}\)*100 = \(\frac{810}{1000}\)*100 = 81%

Kudos [?]: 8 [0], given: 37

Re: The value of a precious stone is directly proportional to the cube of   [#permalink] 19 Nov 2017, 12:48
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The value of a precious stone is directly proportional to the cube of

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