Mid-Project Replacement and Net Team Size 12 men can finish a job in 9 days. After 3 days, 6 men join to replace 2 men (net change in team size). How many more days are needed to finish the remaining work?

Introduction / Context:
The statement “6 men joined to replace 2 men” implies 2 left and 6 joined, so the new team size is 12 − 2 + 6 = 16. Use total man-days and phase-wise accounting to compute the remaining time with the new team size.

Given Data / Assumptions:

• Total work with 12 men in 9 days ⇒ 12*9 = 108 man-days.
• First 3 days at 12 men ⇒ 36 man-days completed.
• After that, effective team size = 16 men.

Concept / Approach:
Remaining man-days divided by the new daily capacity (16) gives the remaining time.

Step-by-Step Solution:
Remaining work = 108 − 36 = 72 man-days.Days needed with 16 men = 72 / 16 = 4.5 days = 4 1/2 days.

Verification / Alternative check:
Fractional days are acceptable because the last day need not be whole; work is continuous.

Why Other Options Are Wrong:
2, 3, and 4 days are too few; 5 is too many relative to 72 man-days and 16 men.

Common Pitfalls:
Misreading “replace” as net zero change; the wording indicates 2 left and 6 joined, producing a net +4 men.

Final Answer:
4 1/2