Question

Monthly expenditure of a person is directly proportional to his monthly income. When the expenditure is Rs 6300 his monthly income is Rs 9000. Find the monthly expenditure when his income is Rs 15000.

Answer 1

$$\begin{gathered} \mathrm{Let}E\mathrm{and}I\mathrm{denote}\mathrm{the}\mathrm{monthly}\mathrm{expenditure}\mathrm{and}\mathrm{monthly}\mathrm{income},\mathrm{respectively}. \\ Thus,wehave: \\ E\alpha I \\ \therefore E=kI\left(k\mathrm{is}\mathrm{constant}.\right) \\ \Rightarrow 6300=k\times 9000\left(E=\mathrm{Rs}6300andI=\mathrm{Rs}9000\right) \\ \Rightarrow k=\frac{6300}{9000} \\ \Rightarrow k=\frac{7}{10} \\ \therefore E=\frac{7}{10}\times I\left(\mathrm{Equation}\mathrm{of}\mathrm{variation}\right) \\ \Rightarrow E=\frac{7}{10}\times 15000\left(\because I=\mathrm{Rs}15000\right) \\ \Rightarrow E=\mathrm{Rs}10500 \end{gathered}$$