The average expenditure of a man for the first five months is ₹ 1200 and for the next seven months is ₹ 1300. If he saves ₹ 2900 in that year, his monthly average income is

### Concept & Formula This problem revolves around the fundamental financial equation: $$ \text{Total Income} = \text{Total Expenditure} + \text{Total Savings} $$ Once the total annual income is found, finding the monthly average is a simple division by $12$. ### Step-by-Step Solution * **Given:** * Average expenditure for first $5$ months = ₹ $1200$ * Average expenditure for next $7$ months = ₹ $1300$ * Total savings for the year = ₹ $2900$ * **Calculation / Deduction:** 1. Calculate the total expenditure for the first $5$ months: $5 \times 1200 = \text{₹ } 6000$ 2. Calculate the total expenditure for the remaining $7$ months: $7 \times 1300 = \text{₹ } 9100$ 3. Find the total annual expenditure: $6000 + 9100 = \text{₹ } 15100$ 4. Calculate the total annual income: $\text{Income} = \text{Expenditure} + \text{Savings}$ $\text{Annual Income} = 15100 + 2900 = \text{₹ } 18000$ 5. Determine the average monthly income: $\text{Monthly Average} = \frac{18000}{12} = \text{₹ } 1500$ ### Exam Strategy & Shortcut While the multiplication here is relatively straightforward, you can use the **Base Average** approach to streamline the expenditure calculation. Assume the base expenditure for all $12$ months is $1200$. The total base expenditure $= 12 \times 1200 = 14400$. The last $7$ months have an excess of $+100$ each, adding $7 \times 100 = 700$. Total expenditure $= 14400 + 700 = 15100$. Add the savings ($2900$) to get $18000$, and divide by $12$ to get $1500$. This keeps the mental arithmetic slightly smaller. ### Common Pitfall The most frequent error is calculating the average expenditure and equating that directly to income, completely forgetting to factor in the savings. Always remember that Income is the sum of *both* what is spent and what is kept. ### Final Answer Therefore, the correct answer is **₹ 1500**.