Inverse Variation – Changing workforce: A certain number of men can complete a job in 80 days. If there were 10 fewer men, the job would require 20 additional days (i.e., 100 days). How many men were there initially?

Introduction / Context:
Work completion time varies inversely with the number of workers when each worker’s productivity is constant. This becomes a simple equation in “man-days”.

Given Data / Assumptions:

• Let initial men = M.
• Initial time = 80 days.
• With 10 fewer men (M − 10), time = 100 days.

Concept / Approach:
Equate man-days: M * 80 = (M − 10) * 100 and solve for M.

Step-by-Step Solution:
80M = 100M − 10001000 = 20MM = 50

Verification / Alternative check:
Man-days = 50 * 80 = 4000. With 40 men: 4000/40 = 100 days, consistent with the condition.

Why Other Options Are Wrong:
45, 40, 60, and 55 fail the man-day equality when checked back against both scenarios.

Common Pitfalls:
Adding times instead of equating man-days; forgetting to multiply by the changed workforce size.

Final Answer:
50