If m men, working m hours per day, can complete exactly m units of work in m days, then in n days how many units of work will be completed by n men working n hours per day? (Assume work ∝ men * hours/day * days and the same job type.)

Introduction / Context:
This question tests direct proportion reasoning in time and work. When task type and productivity conditions remain identical, total work completed varies directly with the product of number of workers, effective hours per day, and the number of days.

Given Data / Assumptions:

• Case 1: m men, m hours/day, m days produce m units.
• Case 2: n men, n hours/day, n days produce X units (unknown).
• Same job environment and linear productivity with respect to men and hours.

Concept / Approach:
Let k be the proportionality constant so that Work = k * (men * hours/day * days). Use Case 1 to determine k, then apply to Case 2.

Step-by-Step Solution:

Verification / Alternative check:
If n = m, then result gives m units, matching the first scenario, so the expression is consistent.

Why Other Options Are Wrong:

• m^3 / n^2: Inverts dependence and breaks symmetry when n = m.
• m^4 / n^2: Has incorrect powers and dimensions.
• n^4 / m^3: Incorrect exponent pattern; fails dimensionally with proportional reasoning.
• None of these: Incorrect because a correct closed form exists.

Common Pitfalls:
Confusing units or assuming work depends on men + hours + days instead of the product men * hours * days; forgetting to solve for the proportionality constant before substitution.

Final Answer:
n^3 / m^2