Suppose a small village consists of only four families. The monthly incomes of three of these families are $₹ 7, 000$ , $₹ 8, 000$ , and $₹ 10, 000$ . If the average per capita monthly income of the village is $₹ 9, 000$ , calculate the monthly income of the fourth family.

medium 3 marks Class 10 · Economics · Development

Answer

₹ 11, 000

The correct answer is $₹ 11, 000$ — Step 5: Solve for $x$ by subtracting $25, 000$ from $36, 000$ : $x = 36, 000 - 25, 000 = 11, 000$ .

Step-by-step solution

Step 1: Recall the formula for average income: $Average Income = \frac{Total Income of All Families}{Total Number of Families}$ .
Step 2: Substitute the given values into the formula, letting $x$ be the monthly income of the fourth family: $9, 000 = \frac{7 , 000 + 8 , 000 + 10 , 000 + x}{4}$ .
Step 3: Multiply both sides by $4$ to find the total income of all four families: $36, 000 = 7, 000 + 8, 000 + 10, 000 + x$ .
Step 4: Sum the incomes of the three known families: $7, 000 + 8, 000 + 10, 000 = 25, 000$ .
Step 5: Solve for $x$ by subtracting $25, 000$ from $36, 000$ : $x = 36, 000 - 25, 000 = 11, 000$ .

Common mistake: Dividing the sum of the three given incomes by

3

instead of using the formula for four total families.

Concept tested: Calculation of per capita income