A precious stone was accidentally dropped and broke into 3 stones of

Question

A precious stone was accidentally dropped and broke into 3 stones of equal weight. The value of this type of stone is always proportional to the square of its weight. The 3 broken stones together are worth how much of the value of the original stone?

(A) 1/9
(B) 1/3
(C) 1
(D) 3
(E) 9

(A) 1/9
(B) 1/3
(C) 1
(D) 3
(E) 9

Archit3110 · Answer

let original weight of stone = 9 value ; 81
so new three pieces ; 3 each and total value ; 9+9+9 ; 27
so new stone value together ; 27/81 ; 1/3
IMO B

yashmehta27101995 · Answer

Let the initial mass be 3kg, then the mass of each broken stone is 1kg each. Since value is directly proportional to square of it's weight, so value of each broken stone is 1^2 x 3 = 3, and of orignal is 3^2 = 9, hence answer B 1/3

Kinshook · Answer

Given:  A precious stone was accidentally dropped and broke into 3 stones of equal weight. The value of this type of stone is always proportional to the square of its weight. 
 Asked:  The 3 broken stones together are worth how much of the value of the original stone?

A precious stone was accidentally dropped and broke into 3 stones of equal weight.
Let the weight of broken stone be x each
Weight of original stone = 3x

The value of this type of stone is always proportional to the square of its weight. 
Value of each broken stone =  kx^2  
Value of 3 broken stones =  3kx^2

Weight of original stone = 3x
The value of original stone = k (3x)^2 = 9kx^2

The 3 broken stones together are worth how much of the value of the original stone = \frac{3kx^2}{9kx^2} = \frac{1}{3}

IMO B

Soz · Answer

We can easily find the answer by plugging in numbers. 
Let the original weight of the stone be 3Kg Hence value will be 3^2 =9{Since the value is proportional to the square of the weight}

The stone is broken into three equal pieces.Therefore weight of each piece will be 1/3*3=1KG
Value of each piece = 1^2=1
Value of three such pieces = 1+1+1=3

Hence ratio of value of sum of pieces to the original stone = 3/9= 1/3.

A precious stone was accidentally dropped and broke into 3 stones of

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