The average expenditure of a man for the first five months of a year is ₹ 5000 and for the next seven months it is ₹ 5400. He saves ₹ 2300 during the year. His average monthly income is

### Concept & Logic Income is fundamentally the sum of Expenditure and Savings. To find the average monthly income, we must first determine the **Total Annual Income** (Total Annual Expenditure + Total Annual Savings) and then divide it by 12 months. $$Total \ Income = Total \ Expenditure + Total \ Savings$$ ### Step-by-Step Solution * **Given:** * Average expenditure for first 5 months = ₹ 5000. * Average expenditure for next 7 months = ₹ 5400. * Total savings for the year = ₹ 2300. * **Calculate Total Annual Expenditure:** * Expenditure for first 5 months = $5 \times 5000 = 25000$. * Expenditure for next 7 months = $7 \times 5400 = 37800$. * Total Annual Expenditure = $25000 + 37800 = 62800$. * **Calculate Total Annual Income:** * Total Annual Income = Total Expenditure + Total Savings * Total Annual Income = $62800 + 2300 = 65100$. * **Calculate Average Monthly Income:** * Average Monthly Income = $\frac{65100}{12}$ * Average Monthly Income = $5425$. ### Exam Strategy & Shortcut Instead of finding massive annual totals, use the **Base Average Method**. 1. Assume the base average monthly income is ₹ 5000. 2. For the first 5 months, the expenditure is exactly the base, so deviation is 0. 3. For the next 7 months, expenditure is ₹ 5400, which is an excess of ₹ 400 per month. Total excess = $7 \times 400 = 2800$. 4. Total savings for the year is ₹ 2300. This is also part of the income. 5. Total "extra" money above the ₹ 5000 base for the whole year = $2800 \text{ (from expenses)} + 2300 \text{ (from savings)} = 5100$. 6. Distribute this ₹ 5100 evenly across 12 months: $\frac{5100}{12} = 425$. 7. True average monthly income = Base ($5000$) + Distributed Extra ($425$) = ₹ 5425. ### Common Pitfall The most common mistake is forgetting to add the annual savings before dividing by 12. Students often calculate the average monthly expenditure ($\frac{62800}{12} \approx 5233.33$) and get confused when it doesn't match the options, forgetting that Income = Expenditure + Savings. ### Final Answer **Therefore, the correct answer is ₹ 5425.**