A farmer spends $75\%$ of his annual income on agricultural inputs and household expenses, saving the remaining portion. In the subsequent year, his income increases by $20\%$, and his expenditure increases by $10\%$. What is the percentage increase in his annual savings? ________ % (answer in integer).
Answer Key:
50
Step-by-Step Solution & Explanation
**Method 1: Tabular Base Model**
- Initial Income $= 100$
- Initial Expenditure $= 75$
- Initial Savings $= 100 - 75 = 25$
In the second year:
- New Income $= 100 \times 1.20 = 120$
- New Expenditure $= 75 \times 1.10 = 82.5$
- New Savings $= 120 - 82.5 = 37.5$
$\text{Increase in Savings} = 37.5 - 25 = 12.5$
$\text{Percentage Increase in Savings} = \frac{12.5}{25} \times 100 = 50\%$
Integer answer: 50.