The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 : 9. How much loss percent is incurred due to this breakage? (Correct to two decimal places)

Solution (By Examveda Team)

$$\eqalign{ & P \propto \sqrt W \cr & {P^2} \propto W \cr & {\text{If weight}} = 14{\text{ gm}} = 5:9 \cr & {\text{Price}} = {5^2} + {9^2} = 106 \cr & {\text{Loss}} = 196 - 106 = 90 \cr & {\text{Loss }}\% = \frac{{90}}{{196}} \times 100 \cr & = 45.918 \cr & = 45.92\% \cr} $$