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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 17 Jun 2019, 23:46
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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 18 Jun 2019, 00:48
Bunuel 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%


Previous weight = 1x+4x+5x=10x; value= 1000x^3
Now value = x^3+64X^3+125x^3=190x^3
Deop in value is 810x^3 as against 1000x^3 previously so IMO D
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New post 18 Jun 2019, 05:11
This is a very good question on proportionality concepts. It also tests your knowledge of interpretation of ratios and percentage change concepts.
Let V be the value of the precious stone whose weight is w. Then,

V \(\alpha\) \(w^3\).

Introducing a constant of proportionality, this becomes,

V = k * \(w^3\).

The big stone has been broken into three parts in the ratio of 1:4:5. The actual weights of these three parts could be x, 4x and 5x. This means, the weight of the big stone should have been 10x (because it’s the sum of these 3 pieces). Therefore,

Value of big stone, \(V_b\) = k \((10x)^3\) = 1000k\(x^3\)

Value of 1st piece, \(V_1\) = k\((x)^3\)

Value of 2nd piece, \(V_2\) = k\((4x)^3\) = 64k\(x^3\)

Value of 3rd piece, \(V_3\) = k\((5x)^3\) = 125k\(x^3\)

The drop in the value of the stone = 1000k\(x^3\) – (k\(x^3\) + 64k\(x^3\) + 125k\(x^3\))

= 1000k\(x^3\) – 190k\(x^3\)
.
= 810k\(x^3\).

Therefore, percentage value in the drop of the stone = 810k\(x^3\) / 1000 k\(x^3\) = 81%.
The correct answer option is D.

A point to note is that you do not have to calculate the values of k or x to solve this question. So, when you draw the first equation, do not set out with the mindset that you solve for the variables because that’s not what is required to answer this question.

Hope this helps!
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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 18 Jun 2019, 09:51
Bunuel 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%


let initial weight = 20 so its value ; 8*10^3
later 1:4:5 the weight would be 2,8,10 respectively
and value 8+512+1000 ; 1520
so % drop in value ; 8000-1520/8000 = 81%
IMO 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 18 Jun 2019, 11:35
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Bunuel 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%


Total weight of the piece is 1 + 4 + 5 = 10 ; so value of the cube is 10^3 = 1000

Value of individual pieces is 1^ + 4^3 + 5^3 = 1 + 64 + 125 = 190

SO, the drop in value is 1000 - 190 = 810 ; Thus, there is 81% drop in the value of the precious stone, Answer must be (D)
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The value of a precious stone is directly proportional to the cube of  [#permalink]

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New post 30 Jun 2019, 07:42

Solution


Given:
• 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

To find:
• The percentage drop in the value of the stone

Approach and Working Out:
    • Initial value = \((10x)^3 = 1000x^3\)• Final value = \(x^3 + (4x)^3 + (5x)^3 = 190x^3\)
    Percentage drop in value = \(\frac{(1000x^3 – 190x^3)}{1000x^3}\) = 81%

Hence, the correct answer is Option D.

Answer: 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 18 Jan 2020, 04:21
Bunuel 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%


We can let the weight of the big stone be 10 grams and its value be $1000.
Since now the stone is broken into 3 parts with weights of 1 gram, 4 grams and 5 grams, the 1-gram stone is worth 1(1)^3 = $1, the 4-gram stone is worth 1(4)^3 = $64 and the 5-gram stone is worth 1(5)^3 = $125. So the total value of the 3 smaller stones is 1 + 64 + 125 = $190, which is only 19% of the original value of $1000. In other words, the value of the stone is reduced by 81%.

Answer: D
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Re: The value of a precious stone is directly proportional to the cube of   [#permalink] 18 Jan 2020, 04:21
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