Scaling harvested area with men and days: If 8 men can reap 80 hectares in 24 days at a constant rate, then how many hectares can 36 men reap in 30 days under similar conditions?

Introduction / Context:When individual efficiency is constant, total output is proportional to the product of workers and days. This question scales a known production to a larger workforce and longer time, applying the unitary method directly to compute the new harvested area.

Given Data / Assumptions:

• Scenario 1: 8 men, 24 days → 80 hectares
• Scenario 2: 36 men, 30 days → ? hectares
• Efficiency per man per day is constant; field conditions are the same.

Concept / Approach:First find the per-man-per-day productivity, then multiply by the new number of men and days. Alternatively, use a direct proportion with a scaling factor comparing the two scenarios.

Step-by-Step Solution:Per man per day = 80 / (8 * 24) = 80 / 192 = 5/12 haOutput for 36 men, 30 days = (5/12) * 36 * 30 = 5 * 3 * 30 = 450 ha

Verification / Alternative check:Scale factors: men × days multiplier = (36/8) * (30/24) = 4.5 * 1.25 = 5.625; 80 * 5.625 = 450 ha. Same result confirms validity.

Why Other Options Are Wrong:350, 425, 400, and 460 do not equal 80 * 5.625; only 450 matches the proportional scaling precisely.

Common Pitfalls:Mixing up the direction of the ratio or forgetting to apply both workforce and time scale factors together.

Final Answer:450