Output changes with manpower and time: 20 men can cut 30 trees in 4 hours. If 4 men leave (so 16 men remain), how many trees will be cut in 12 hours by the remaining men (assume proportional output)?

Introduction / Context:
When output is proportional to the product of (number of workers) * (time), we can find a per man-hour productivity and scale it to any new combination of workers and hours. This is a direct application of the “work is proportional to man-hours” model.

Given Data / Assumptions:

• With 20 men in 4 hours, trees cut = 30.
• Assume constant productivity per man-hour across scenarios.
• New scenario: 16 men for 12 hours.

Concept / Approach:
Compute trees per man-hour first: trees / (men * hours). Then multiply by the new man-hour total to get the output for the changed team and duration.

Step-by-Step Solution:

Verification / Alternative check:
Proportional scaling: Men reduced by factor 16/20 = 0.8, hours increased by 12/4 = 3; overall scale = 0.8 * 3 = 2.4; thus trees = 30 * 2.4 = 72, same result.

Why Other Options Are Wrong:
80 and 79 exceed the proportional output; 68 and 64 are too low given the large increase in total man-hours.

Common Pitfalls:
Forgetting to scale both men and hours, or assuming linearity in one but not the other. Output is proportional to their product under constant productivity.

Final Answer:
72