A man spends 80% of his income. With increase in the cost of living, his expenditure increases by 371/2 % and his income increases by 162/3 %. His present savings are :

Answer: Option B

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 :
$$\begin{array}{rl}& =\text{Rs}\text{.}\left(\frac{350}{3}-110\right)\\ & =\text{Rs}\text{.}\frac{20}{3}\end{array}$$
∴ Required percentage
$$\begin{array}{rl}& =\left(\frac{20}{3}\times \frac{3}{350}\times 100\right)\%\\ & =\frac{40}{7}\%\\ & =5\frac{5}{7}\%\end{array}$$