Three people A, B, and C have these annual average income pairs: Average(A, B) = ₹80,000 Average(B, C) = ₹75,000 Average(C, A) = ₹78,000 Find the annual income of A (in ₹).

Introduction / Context:
This problem tests average-based equations. Pairwise averages can be converted into pairwise sums. Once you have the sums (A+B), (B+C), and (C+A), you can combine them to get A+B+C and then isolate A.

Given Data / Assumptions:

• (A + B)/2 = 80,000
• (B + C)/2 = 75,000
• (C + A)/2 = 78,000
• All incomes are annual and measured in ₹.

Concept / Approach:
Convert averages to sums: A + B = 2*80,000 B + C = 2*75,000 C + A = 2*78,000 Then add all three equations. The left side becomes 2(A + B + C). Solve for A by subtracting (B + C) from (A + B + C).

Step-by-Step Solution:

Verification / Alternative check:
If A = 83,000 then A + B = 160,000 implies B = 77,000. Then B + C = 150,000 gives C = 73,000. Check C + A = 73,000 + 83,000 = 156,000 which matches the third equation.

Why Other Options Are Wrong:

Common Pitfalls:
Forgetting that the average of two numbers is half their sum, or adding averages directly without converting to sums first.

Final Answer:
₹83,000