Peter could save 10% of his income. But two years later when his income is increased by 20%, he could save the same amount only as before. By how much percent has his expenditure increased?

Concept & Logic This problem revolves around the basic financial equation: $$Income = Expenditure + Savings$$ To find the percentage increase in expenditure, we need to compare the initial expenditure with the new expenditure after the income changes, keeping the absolute savings constant. Step-by-Step Solution * **Initial State:** Let Peter's initial income be ₹ 100. Savings = $10\%$ of $100$ = ₹ 10. Expenditure = Income - Savings = $100 - 10$ = ₹ 90. * **New State:** His income increases by $20\%$. New Income = $100 + 20$ = ₹ 120. He saves the *same amount* as before. New Savings = ₹ 10. New Expenditure = New Income - New Savings = $120 - 10$ = ₹ 110. * **Calculation of Percentage Increase:** Increase in Expenditure = New Expenditure - Initial Expenditure Increase = $110 - 90 = 20$. $$\text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Initial Expenditure}} \right) \times 100$$ $$Percentage Increase = \left( \frac{20}{90} \right) \times 100$$ $$Percentage Increase = \frac{200}{9}\% = 22 \frac{2}{9}\%$$ Exam Strategy & Shortcut Assume a convenient base value like 100 for income. This immediately yields an initial expenditure of 90. When income goes to 120 and savings are locked at 10, the new expenditure must be 110. The jump from 90 to 110 is an increase of 20 over a base of 90, which is $\frac{2}{9}$. Knowing your fraction-to-percentage conversions ($\frac{1}{9} = 11.11\%$), $\frac{2}{9}$ is instantly $22.22\%$, or $22 \frac{2}{9}\%$. Common Pitfall A common error is calculating the percentage increase over the *new* expenditure (110) or the original *income* (100) instead of the original *expenditure* (90). Always calculate percentage increase based on the original starting value of the specific metric being asked about. Final Answer **Therefore, the correct answer is $22 \frac{2}{9}\%$.**