Missing workers from day one change the timeline A contractor plans to complete a job in 18 days with a certain number of men. However, 12 men are absent from the very first day and the remaining crew finishes the work in 30 days. How many men were originally planned?

Introduction / Context:
This is a classic “planned strength vs. actual strength” time and work problem. We equate total work using rate * time with different crew sizes.

Given Data / Assumptions:

• Planned duration = 18 days with M men.
• Actual: (M − 12) men finish in 30 days.
• Each man has the same constant productivity.

Concept / Approach:
Let a single man’s daily rate be r. Total work W can be written two ways and equated.

Step-by-Step Solution:

Verification / Alternative check:
Plug back: Planned capacity per day = 30r; in 18 days gives 540r. Actual capacity per day = 18r; in 30 days gives 540r. Matches.

Why Other Options Are Wrong:

• 40, 24, 18: Do not satisfy the equation 18M = 30(M − 12).
• None of these: Incorrect because 30 fits perfectly.

Common Pitfalls:
Forgetting to hold total work constant or mixing up which team size applies to which duration.

Final Answer:
30