Discussion Forum

The cost of diamond varies as the square of its weight. A diamond weighing 10 decigrams costs Rs.32000. Find the loss incurred when it breaks into two pieces whose weights are in the ratio 2 : 3

Answer:

Explanation:

The diamond breaks into two pieces in the ratio 2: 3

Weight of first piece = $\frac{2}{5}\times10$ = 4 decigrams

Weight of second piece = $\frac{3}{5}\times10$ = 6 decigrams

Given,cost of diamond varies as square  of its weight.

Cost of the original diamond  $\propto 10^{2}$

Cost of original diamond = 100 k

Cost of first piece $\propto 4^{2}$

=16 k

Similarly cost of second piece = 36 k

Total cost of two  piece = 16+36 k= 52k

Loss in total value of diamond = 100 k – 52 k = 48k

But, 100k = 32000

K= 320

Loss incurred = 48k

$= 48\times 320$ = 15360