Scaling workforce and scope: Some persons can complete a job in 12 days. If the number of persons is doubled, how long will it take to complete half of that job?

Introduction / Context:For fixed productivity, time varies directly with work and inversely with manpower. Here both the team size and the amount of work change, so we combine both effects carefully.Given Data / Assumptions:

• Original: N persons finish the full job in 12 days.
• New plan: 2N persons, and only half of the original job.

Concept / Approach:Total work W = N * 12 (person-days). Half work is W/2. With 2N persons, time t = (W/2) / (2N) = W / (4N). Substitute W = 12N to solve.Step-by-Step Solution:

Verification / Alternative check:Check proportionality: doubling persons halves the time; halving the work halves the time again. Starting from 12 days: 12/2/2 = 3 days.

Why Other Options Are Wrong:

• 16, 12, 8: Ignore the compounded effect of both changes (work halved and manpower doubled).

Common Pitfalls:Applying only one of the two changes or adding/dividing in the wrong order. Always express in person-days to avoid confusion.

Final Answer: