Recovering a deceased member’s income from changing family averages: The average monthly income of 4 earning members of a family is ₹7350. After one member passes away, the average monthly income becomes ₹6500 for the remaining 3 members. What was the monthly income of the member who passed away?

Introduction / Context:
Averages convert to totals seamlessly. With the original four-member average and the new three-member average, we can find the lost member’s contribution as the difference between totals.

Given Data / Assumptions:

• 4-member average = ₹7350 → total = ₹29400
• 3-member average = ₹6500 → total = ₹19500

Concept / Approach:
Income of the deceased = original total − new total.

Step-by-Step Solution:
Original total = 4 * 7350 = ₹29400New total = 3 * 6500 = ₹19500Missing income = ₹29400 − ₹19500 = ₹9900

Verification / Alternative check:
Re-add ₹9900 to the remaining totals: (₹19500 + ₹9900) / 4 = ₹29400 / 4 = ₹7350, consistent.

Why Other Options Are Wrong:
Other values do not reconcile the two totals to the given averages.

Common Pitfalls:
Mistaking an average change as a per-person change; always work with totals first.

Final Answer:
₹ 9900