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: