A man spends 80% of his income. With increase in cost of living, his expenditure increases by $$37\frac{1}{2}$$% and his income increases by $$16\frac{2}{3}$$%. His present savings are :

Let original income = Rs. 100
Then, saving = Rs. 20 and expenditure = Rs. 80
New income :
$$=$$ Rs. $$116\frac{2}{3}$$
$$=$$ Rs. $$\frac{350}{3}$$
New expenditure :
$$=$$ $$137\frac{1}{2}$$ % of Rs. 80
$$=$$ Rs. $$\left( {\frac{{275}}{2} \times \frac{1}{{100}} \times 80} \right)$$
$$=$$ Rs. 110
New saving :
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{350}}{3} - 110} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{20}}{3} \cr} $$
∴ Required percentage
$$\eqalign{ & = \left( {\frac{{20}}{3} \times \frac{3}{{350}} \times 100} \right)\% \cr & = \frac{{40}}{7}\% \cr & = 5\frac{5}{7}\% \cr} $$