Scaling wall construction with men, length, and hours: 40 men build a 200 m wall in 12 days working 8 h/day. How many days will 30 men take to build a similar 300 m wall working 6 h/day (assume proportional productivity)?

Introduction / Context: In uniform construction tasks, output is proportional to the product of (number of men) * (days) * (hours per day). First deduce the man-hour requirement per meter from the base scenario, then use it to compute the required man-days when the workforce and daily hours change and the length increases to 300 m.

Given Data / Assumptions:

• Base: 40 men, 12 days, 8 h/day build 200 m.
• New: 30 men, 6 h/day, length = 300 m.
• Productivity assumed constant (similar wall, same conditions).

Concept / Approach: Compute man-hours per meter from the base case. Then total man-hours needed for 300 m equals (man-hours/m) * 300. Divide by daily man-hours (men * hours/day) to obtain the number of days for the new scenario.

Step-by-Step Solution:

Verification / Alternative check: Ratio method: Scale by length (300/200 = 1.5), inverse by men (40/30 = 4/3), and inverse by hours (8/6 = 4/3). Days_new = 12 * 1.5 * (40/30) * (8/6) = 12 * 1.5 * 4/3 * 4/3 = 32, consistent.

Why Other Options Are Wrong: 18, 36, 9, or 28 days do not satisfy the man-hour balance and proportional scaling across all factors.

Common Pitfalls: Ignoring the change in daily working hours or scaling only by men and length without adjusting for hours per day.

Final Answer: 32