Scaling manpower to meet a deadline: 40 men complete one-third of a job in 40 days. How many additional men are needed to finish the remaining work in 50 more days (constant rates)?

Introduction / Context:
As with all man-day problems, compute total work units from the partial completion, determine the required manpower for the remaining work within the new deadline, and then find the additional men beyond the current team size.

Given Data / Assumptions:

• 40 men finish 1/3 of the job in 40 days.
• Remaining work = 2/3.
• Remaining time allowed = 50 days.

Concept / Approach:
Let r be a man’s daily rate, W total work. From 40*40*r = W/3, determine r in terms of W. Then compute the men needed to do 2W/3 in 50 days, and subtract 40 to get the additional men.

Step-by-Step Solution:

Verification / Alternative check:
Man-days remaining = (2/3)W = (2/3)*(4800r) = 3200r. In 50 days ⇒ men/day = 3200r/50 = 64r ⇒ 64 men, consistent with the above.

Why Other Options Are Wrong:
12, 18, 20, 28 do not match the required man-day balance for a 50-day completion window.

Common Pitfalls:
Not subtracting the existing workforce from total men required, or mixing up the one-third and two-thirds portions of the job.

Final Answer:
24