Question

the value of diamond varies with the square of it's weight. A Rs.14,40,000 worth diamond breaks into three pieces whose weight are in the ratio 3:4:5. The loss in its value due to breakage (in lakhs) is?

Answer 1

Price of diamond = Rs.5184. As price is proportional to square of  weight of diamond, weight of diamond = √5184 = 72.
This weight of 72 units is divided in the ratio 1 : 2 : 3.
Hence their weights are (1/6)x72, (2/6)x72, (3/6)x72v OR 12, 24, 36 units by weight.

Hence their price are 12², 24², 36² , i.e., 144, 576, 1296.
Hence total price of three pieces = 144+576+1296 = 2016.
Therefore loss involved in cutting = 5184 - 2016 = 3168