Income Calculation: Understanding Average Monthly Income

This problem involves calculating the total monthly income of three individuals, A, B, and C, given the average monthly incomes of pairs of them.

Defining Variables for Monthly Income

Let's represent the monthly income of each person using variables:

• Let $A$ be the monthly income of person A.
• Let $B$ be the monthly income of person B.
• Let $C$ be the monthly income of person C.

Deriving Sums from Average Incomes

We are given the average monthly incomes for pairs of individuals. We can use the definition of average (sum of values divided by the number of values) to find the sum of incomes for each pair.

• Average income of A and B: The average is given as ₹5,050. $$ \frac{A + B}{2} = 5050 $$ Multiplying both sides by 2, we get the sum of A's and B's income: $$ A + B = 2 \times 5050 = 10100 \quad \text{(Equation 1)} $$
• Average income of B and C: The average is given as ₹6,250. $$ \frac{B + C}{2} = 6250 $$ Multiplying both sides by 2, we get the sum of B's and C's income: $$ B + C = 2 \times 6250 = 12500 \quad \text{(Equation 2)} $$
• Average income of A and C: The average is given as ₹5,200. $$ \frac{A + C}{2} = 5200 $$ Multiplying both sides by 2, we get the sum of A's and C's income: $$ A + C = 2 \times 5200 = 10400 \quad \text{(Equation 3)} $$

Calculating the Total Sum of Monthly Incomes

To find the total sum of the monthly incomes of A, B, and C (i.e., $A + B + C$), we can add the three equations derived above:

Adding Equation 1, Equation 2, and Equation 3:

Combine like terms on the left side:

Factor out 2 from the left side:

Finally, divide both sides by 2 to find the sum of the monthly incomes of A, B, and C:

Therefore, the sum of the monthly incomes of A, B, and C is ₹16,500.