Question

The cost price of sugar is directly proportional to its weight. Cost of 12 kg. of sugar is Rs. 360. Find the cost of 5 kg. of sugar.

Answer 1

$$\begin{gathered} \mathrm{Let}C\mathrm{and}W\mathrm{denote}\mathrm{the}\mathrm{cost}\mathrm{price}\mathrm{and}\mathrm{weight}\mathrm{of}\mathrm{sugar},\mathrm{respectively}. \\ Thus,wehave: \\ C\alpha W \\ \Rightarrow C=kW\left(H\mathrm{ere},k\mathrm{is}\mathrm{constant}.\right) \\ \Rightarrow 360=k\times 12\left(C=\mathrm{Rs}360andW=12\mathrm{kg}\right) \\ \Rightarrow k=30 \\ Or, \\ C=30W\left(\mathrm{Equation}\mathrm{of}\mathrm{variation}\right) \\ \therefore C=30\times 5\left(\because W=5\mathrm{kg}\right) \\ \Rightarrow C=\mathrm{Rs}150 \end{gathered}$$