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)?
Correct Answer: 12
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:
Given: 20 men * 20 days * r = W/3 ⇒ 400r = W/3 ⇒ r = W/1200 Let M be men needed for the remaining 2W/3 in 25 days: M * 25 * r = 2W/3 M = (2W/3) / (25r) = (2/3) * (1200/25) = 32 men (total) Extra men required = 32 − 20 = 12Verification / 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