The average revenues of a company over seven consecutive years is Rs 79 lakhs. The average of the first four years is Rs 74 lakhs and the average of the last four years is Rs 86 lakhs. What is the revenue in the 4th year?

Introduction:
This classic sliding-window average problem uses the fact that the 4th year is included in both the first four-year block and the last four-year block. Summing those blocks and subtracting the seven-year total isolates the shared year's revenue.

Given Data / Assumptions:
Avg of 7 years = 79 ⇒ total of 7 years = 7 * 79 = 553 lakhs. Avg of first 4 years = 74 ⇒ sum(first four) = 296 lakhs. Avg of last 4 years = 86 ⇒ sum(last four) = 344 lakhs.

Concept / Approach:
The 4th year appears in both four-year sums. Therefore, revenue in year 4 = sum(first four) + sum(last four) − sum(all seven).

Step-by-Step Solution:
Revenue in 4th year = 296 + 344 − 553 = 87 lakhs.

Verification / Alternative check:
Constructing a symbolic sequence Y1..Y7 with the two window sums confirms that only Y4 remains after subtraction, validating the formula.

Why Other Options Are Wrong:
89, 85, 83, 81 lakhs: None satisfy the overlapping-window identity with the given averages.

Common Pitfalls:
Averaging the two window averages (74 and 86) to get 80, which ignores the overlap and is incorrect. Use totals and the overlap logic instead.

Final Answer:
Revenue in the 4th year is Rs 87 lakhs.