The aggregate monthly expenditure of family was ₹18720 during the first 3 months. ₹20340 during the next 4 months and ₹21708 during the last 5 months of year. If the total savings during the year be ₹35340 find the average monthly income of the family.

Explanation

To find the average monthly income of the family, we will follow these steps:

### Step 1: Calculate the total expenditure for the year.
The family has different expenditures for different periods:
- For the first 3 months: ₹18720 per month
- For the next 4 months: ₹20340 per month
- For the last 5 months: ₹21708 per month

Now, we calculate the total expenditure for each period:
1. **First 3 months**:
\[ \text{Expenditure} = 18720 \times 3 = 56160 \]
2. **Next 4 months**:
\[ \text{Expenditure} = 20340 \times 4 = 81360 \]
3. **Last 5 months**:
\[ \text{Expenditure} = 21708 \times 5 = 108540 \]

### Step 2: Add the total expenditures to find the total expenditure for the year.
Now, we sum up all the expenditures:
\[ \text{Total Expenditure} = 56160 + 81360 + 108540 = 281060 \]

### Step 3: Add the total savings to find the total income.
The total savings during the year is ₹35340. Therefore, the total income can be calculated as follows:
\[ \text{Total Income} = \text{Total Expenditure} + \text{Total Savings} \]
\[ \text{Total Income} = 281060 + 35340 = 316400 \]

### Step 4: Calculate the average monthly income.
To find the average monthly income, we divide the total income by 12 (the number of months in a year):
\[ \text{Average Monthly Income} = \frac{\text{Total Income}}{12} \]
\[ \text{Average Monthly Income} = \frac{316400}{12} = 26366.67 \]

### Final Answer:
The average monthly income of the family is approximately ₹26366.67.

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