Solution:
it is given that the price of a precious stone is directly proportional to the square of its weight. Let the price be denoted by C and the weight is denoted by W.
Hence, C∝W2=C=kw2 (where k is the proportional constant)
Now, Sita has a precious stone weighing 18 units.
Therefore, C=kw2=k⋅182=324
If she breaks it into four pieces with each piece having a distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000 .
To get the lowest possible value of C, we will get the weight of the four-piece as close as possible (3,4,5,6). To get the highest value we will try to take three pieces as low as possible, and one is as high as possible (1,2, 3 , 12).
Hence, the maximum cost =k(122+12+22+32)=158k2, and the minimum cost is k(32+42+52+. 62)=86k2
Hence, the difference is (158k2−86k2)=72k2, which is equal to 288000 .
⇒72k2=288000
⇒k2=4000
Hence, the price of the original stone is 324k2=324×4000=1296000 The correct option is D
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