Men–hours–days scaling: 16 men working 7 hours per day plough a field in 48 days. In how many days will 14 men working 12 hours per day plough the same field?

Introduction / Context:
Total work is proportional to men * hours/day * days when productivity per man-hour is constant. Equate total man-hours across scenarios to find the unknown time for the changed team and schedule.

Given Data / Assumptions:

• Scenario 1: 16 men, 7 h/day, 48 days.
• Scenario 2: 14 men, 12 h/day, D days.
• Productivity per man-hour is constant.

Concept / Approach:
Set man-hours equal: 16*7*48 = 14*12*D, then solve for D. This is a classic men–hours–days proportionality problem under the unitary method.

Step-by-Step Solution:

Verification / Alternative check:
Man-hours in scenario 1 = 16*7*48 = 5376; scenario 2 = 14*12*32 = 5376; equality confirmed.

Why Other Options Are Wrong:
56, 38, 30, 28 do not satisfy the equal-man-hours relation for the same field.

Common Pitfalls:
Multiplying or dividing the wrong factors or forgetting that increasing hours/day allows fewer days for the same total work.

Final Answer:
32