Question

the average expenditure of a man for the first five months of a year is Rs.5000 and for the next seven months is Rs.5400.He saves Rs.2300 during the year.Find his average monthly income

Answer 1

$$\begin{gathered} \mathrm{Average}\mathrm{expenditure}\mathrm{of}\mathrm{first}5\mathrm{months}=\mathrm{Rs}5000 \\ \Rightarrow \frac{\mathrm{Total}\mathrm{expenditure}\mathrm{in}5\mathrm{months}}{5}=5000 \\ \Rightarrow \mathrm{Total}\mathrm{expenditure}\mathrm{in}5\mathrm{months}=\mathrm{Rs}25000 \\ \mathrm{Average}\mathrm{expenditure}\mathrm{of}\mathrm{next}7\mathrm{months}=\mathrm{Rs}5400 \\ \Rightarrow \frac{\mathrm{Total}\mathrm{expenditure}\mathrm{in}\mathrm{next}7\mathrm{months}}{7}=5400 \\ \Rightarrow \mathrm{Total}\mathrm{expenditure}\mathrm{in}\mathrm{next}7\mathrm{months}=\mathrm{Rs}37800 \\ \mathrm{Total}\mathrm{expenditure}\mathrm{in}\mathrm{an}\mathrm{year}=25000+37800=\mathrm{Rs}62800 \\ \mathrm{Now},\mathrm{savings}\mathrm{in}\mathrm{an}\mathrm{year}=\mathrm{Rs}2300 \\ \mathrm{Total}\mathrm{income}\mathrm{in}\mathrm{an}\mathrm{year}=\mathrm{Rs}65100 \\ \mathrm{Average}\mathrm{monthly}\mathrm{income}=\frac{65100}{12}=\mathrm{Rs}5425 \end{gathered}$$