Question

The cost of a precious stone varies as the cube of its weight. The stone broke into 3 pieces whose weights are in the ratio ` 1 : 2 : 3`. As a result its cost reduces . If the cost of the unbroken stone is Rs. 96, 336, then find the loss incurred due to breakage.
A. ` Rs. 80,280`
B. ` Rs. 16,056`
C. ` Rs. 40,140`
D. ` Rs. 8028`

Answer 1

Correct Answer - A
(i) Let the weights of the three pieces be x, 2x and 3x and their costs be `C_(1), C_(2) and C_(3)` respectively .
(ii) `C_(1)/x^(3) = C_(2)/(2x)^(3) = C_(3)/(3x)^(3) = (96, 336)/(6x)^(3)`.
(iii) Find `C_(1),C_(2) and C_(3)` and then `96,336 - (C_(1)+C_(2)+C_(3))`.