The monthly income of a person was Rs. $80,000$ and his monthly expenditure was Rs. $45,000$. Next year, his income increased by $16\%$ and his expenditure increased by $8\%$. Find the percentage increase in his savings (correct to $2$ decimal places).

Let's establish initial values: Initial Income = Rs. $80,000$ Initial Expenditure = Rs. $45,000$ Initial Savings = $\text{Income}-\text{Expenditure}=80,000-45,000=\text{Rs. }35,000$ Now compute the new values after the percentage increases:New Income = $80,000\times (1+0.16)=80,000\times 1.16=\text{Rs. }92,800$ New Expenditure = $45,000\times (1+0.08)=45,000\times 1.08=\text{Rs. }48,600$ New Savings = $92,800-48,600=\text{Rs. }44,200$ Now find the absolute and percentage increase in savings:Increase in Savings = $44,200-35,000=\text{Rs. }9,200$ Percentage Increase = $\left(\frac{9,200}{35,000}\right)\times 100=\frac{920}{35}\%\approx 26.2857\%$ Rounding to two decimal places gives $26.29\%$.