Overlapping four-day averages: A mechanic’s average earning for the first four days of a week is Rs 18, and for the last four days is Rs 22. If he earned Rs 20 on the fourth day, what is his average earning for the entire seven-day week?

Introduction / Context:Two overlapping four-day averages (days 1–4 and days 4–7) allow recovery of the seven-day total if the overlapping day’s value is known. Subtract the overlap once to avoid double-counting.Given Data / Assumptions:

• Average days 1–4 = Rs 18 ⇒ sum1 = 72.
• Average days 4–7 = Rs 22 ⇒ sum2 = 88.
• Day 4 earning = Rs 20.

Concept / Approach:Sum over the week equals sum1 + sum2 minus the overlap day once (because day 4 appears in both sums). Then divide by 7 for the weekly average.Step-by-Step Solution:

Verification / Alternative check:Construct a small example with variables for the unknown days and verify the same relation; algebra reduces exactly to subtracting the overlap once.Why Other Options Are Wrong:

• Rs 18.95, Rs 16, Rs 25.71: Do not match the computed weekly average from correct total 140.

Common Pitfalls:Forgetting day 4 is counted twice in the two four-day blocks; failing to subtract it once leads to an inflated total.Final Answer: