Sixteen men working 18 hours per day can build a wall 36 m long, 4 m wide, and 24 m high in 20 days. How many men are required to build a wall 64 m long, 6 m wide, and 18 m high in 16 days if they work 12 hours per day?

Introduction / Context:
This is a direct proportion problem where required effort is proportional to volume * men * hours * days. Changing any dimension or schedule scales the manpower requirement accordingly.

Given Data / Assumptions:

• Case 1: 16 men, 18 h/day, 20 days → wall 36 × 4 × 24.
• Case 2: Unknown men M, 12 h/day, 16 days → wall 64 × 6 × 18.

Concept / Approach:
Use proportionality: (men * hours * days) ∝ volume. Set up a ratio between cases and solve for M.

Step-by-Step Solution:

Verification / Alternative check:
Volume doubles (6912 vs 3456), but hours/day and days are reduced; the computed M reflects these counterbalancing effects and yields an integer 60.

Why Other Options Are Wrong:
They do not satisfy the proportionality when all factors (hours and days) are correctly accounted for.

Common Pitfalls:
Ignoring one of the scaling factors (hours or days) or mixing up volume dimensions.

Final Answer:
60