Question

The cost of a diamond varies as the square of its weight. A diamond weighing 20 decigrams costs Rs. 4,800. Find the cost of a diamond(in rupees) of the same kind weighing 8 decigrams.

Answer 1

Let $C$ be the cost of the diamond and $W$ be its weight.

Given:Cost of a diamond varies as the square of its weight.

$\Rightarrow C\propto W^2$

$\Rightarrow C=k{W}^2$ where $k$ is the proportionality constant.

Given:A diamond weighing $20$ decigrams costs $Rs.4,800$

$\Rightarrow 4800=k\times {20}^2$

$\Rightarrow 4800=400k$

$\Rightarrow 12=k$

$\Rightarrow k=12$

Now,$C=12\times 8^2$

$\Rightarrow C=12\times 64=768$

$\therefore$ cost of a diamond of the same kind weighing $8$ decigrams is $Rs.768$