Between two consecutive years my incomes are in the ratio of $2 : 3$ and expenses in the ratio $5 : 9$. If my income in the second year is ₹ 45000 and my expenses in the first year is ₹ 25000 my total savings for the two years is

### Concept & Period Segregation Treat each year as a separate calculation block. Find the absolute values for income and expenses for each year using their respective ratios before combining them to find total savings. ### Step-by-Step Solution 1. **Income Analysis:** Ratio of Year 1 to Year 2 income is $2 : 3$. Let incomes be $2x$ and $3x$. 2. Income in Year 2 is ₹ 45000. So, $3x = 45000 \implies x = 15000$. 3. Income in Year 1 is $2x = 2(15000) = 30000$. 4. **Expense Analysis:** Ratio of Year 1 to Year 2 expense is $5 : 9$. Let expenses be $5y$ and $9y$. 5. Expense in Year 1 is ₹ 25000. So, $5y = 25000 \implies y = 5000$. 6. Expense in Year 2 is $9y = 9(5000) = 45000$. 7. **Savings Analysis:** - Savings Year 1 = Income Year 1 - Expense Year 1 = $30000 - 25000 = 5000$. - Savings Year 2 = Income Year 2 - Expense Year 2 = $45000 - 45000 = 0$. 8. Total Savings = Savings Year 1 + Savings Year 2 = $5000 + 0 = 5000$. ### Exam Strategy & Shortcut Year 2 income is 45000 (3 parts), so Year 1 income is 30000 (2 parts). Year 1 expense is 25000 (5 parts), so Year 2 expense is 45000 (9 parts). Year 1 savings = $30k - 25k = 5k$. Year 2 savings = $45k - 45k = 0$. Total = 5000. The numbers are clean enough to compute mentally. ### Common Pitfall Mixing up the ratios by cross-applying the income multiplier to the expense ratio, or forgetting to sum the savings of both years at the end. ### Final Answer Therefore, the correct answer is **₹ 5000**.