Question

The cost of diamond varies as the square of its weight. A diamond weighing 10 decigrams costs Rs. 1600. Find the cost of diamond of the same kind weighing 7 decigrams.

Answer 1

$$\begin{gathered} \mathrm{Let}C\mathrm{denote}\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{the}\mathrm{diamond}\mathrm{and}W\mathrm{denote}\mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{diamond}. \\ C\alpha W^2(\mathrm{Given}) \\ C=K{W}^2(K\mathrm{is}\mathrm{a}\mathrm{constant}.) \\ \mathrm{When}W=10\mathrm{decigram}sandC=\mathrm{Rs}1600, \\ 1600=K{\left(10\right)}^2 \\ 1600=100K \\ K=16...\left(i\right) \\ C=16W^2(\mathrm{Equation}\mathrm{of}\mathrm{variation}) \\ =16\times {\left(7\right)}^2(\because W=7\mathrm{decigrams}) \\ =\mathrm{Rs}784 \end{gathered}$$