Question

The price of diamond varies directly as the square of its weight. The diamond having weight 10 decigrams costing Rs. 4000 broke into two pieces having weight 7 decigrams and 3 decigrams respectively. If both the pieces are sold separately, find whether the merchant will get profit or loss and how much?

Answer 1

$$\begin{gathered} \mathrm{Let}P\mathrm{and}W\mathrm{denote}\mathrm{the}\mathrm{price}\mathrm{and}\mathrm{weight}\mathrm{of}the\mathrm{diamond},\mathrm{respectively}. \\ Thus,wehave: \\ P\alpha W^2 \\ \therefore P=k{W}^2\left(k\mathrm{is}\mathrm{constant}.\right) \\ \Rightarrow 4000=k\times {\left(10\right)}^2\left(P=\mathrm{Rs}4000andW=10\mathrm{decigram}s\right) \\ \Rightarrow k=40 \\ The\mathrm{diamond}\mathrm{is}\mathrm{divided}\mathrm{into}\mathrm{two}\mathrm{pieces},\mathrm{so}\mathrm{we}\mathrm{will}\mathrm{calculate}\mathrm{the}\mathrm{price}\mathrm{of}\mathrm{diamond}\mathrm{for}\mathrm{both}\mathrm{the}\mathrm{cases}\mathrm{separately}. \\ \mathrm{Let}\mathrm{the}\mathrm{price}\mathrm{of}the\mathrm{diamond}\mathrm{weighing}7\mathrm{decigrams}\mathrm{be}{P}_1\mathrm{and}\mathrm{the}\mathrm{price}\mathrm{of}the\mathrm{diamond}\mathrm{weighing}3\mathrm{decigrams}\mathrm{be}{P}_2. \\ \therefore P_1=40\times {\left(7\right)}^2 \\ \Rightarrow P_1=\mathrm{Rs}1960 \\ \therefore P_2=40\times {\left(3\right)}^2 \\ \Rightarrow P_2=\mathrm{Rs}360 \\ \Rightarrow P_1+P_2=\mathrm{Rs}\left(1960+360\right) \\ =\mathrm{Rs}2320 \\ \mathrm{Price}\mathrm{of}\mathrm{the}\mathrm{diamond}\mathrm{before}\mathrm{it}\mathrm{was}\mathrm{broken}\mathrm{into}\mathrm{two}\mathrm{pieces},\mathrm{P}=\mathrm{Rs}4000 \\ \mathrm{Price}\mathrm{of}\mathrm{the}\mathrm{diamond}\mathrm{after}\mathrm{it}\mathrm{was}\mathrm{broken}\mathrm{into}\mathrm{two}\mathrm{pieces},\mathrm{P}=\mathrm{Rs}2320 \\ Totall\mathrm{oss}=\mathrm{Rs}\left(4000-2320\right)=\mathrm{Rs}1680 \end{gathered}$$