Scaling manpower to meet a deadline: 20 men complete one-third of a job in 20 days. How many additional men are required to finish the remaining work in 25 more days (assume constant individual rates)?

Introduction / Context:
Use man-days as the unit of work. First compute the total job in man-days from a known partial completion. Then compute how many men are needed to deliver the remaining man-days within the new deadline, and subtract the existing workforce to find the extra men required.

Given Data / Assumptions:

• 20 men finish 1/3 of the job in 20 days.
• Remaining work = 2/3 of the job.
• Deadline for the remainder = 25 days.

Concept / Approach:
Let r be one man’s daily work and W be total work. From the partial completion, determine r or W/r. Then use rate * time = work to solve for the required team size to finish the remainder in the allotted time.

Step-by-Step Solution:

Verification / Alternative check:
Man-days remaining = (2/3)W = (2/3)*(1200r) = 800r. In 25 days, daily manpower = 800r / 25 = 32r ⇒ 32 total men. This reconfirms the calculation.

Why Other Options Are Wrong:
10, 15, 20, 8 do not satisfy the man-day balance for 25 remaining days.

Common Pitfalls:
Adding or averaging days instead of using man-days, or forgetting to subtract the existing 20 men from the total required.

Final Answer:
12