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

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

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.