Scaling workforce to hit a target: If 40 men make 30 boxes in 20 days, how many more men are needed to make 60 boxes in 25 days (same efficiency)?

Introduction / Context:
This is a direct work-rate proportionality problem. Boxes made are proportional to men * days (assuming identical hours and efficiency). We first compute output per man-day from the first scenario and then determine required men for the new target, finally reporting “how many more” than 40 are needed.

Given Data / Assumptions:

• Base: 40 men make 30 boxes in 20 days
• Target: 60 boxes in 25 days
• Same daily hours and same efficiency

Concept / Approach:
Boxes per man-day = 30 / (40*20). For target, let M men be needed so that M * 25 * (boxes per man-day) = 60. Solve for M, then subtract 40 to get “additional men”.

Step-by-Step Solution:

Verification / Alternative check:
Proportion method: Men ∝ (Boxes)/(Days) with same productivity ⇒ M = 40 * (60/30) * (20/25) = 40 * 2 * 0.8 = 64. Additional = 24. Same result by a quicker ratio approach.

Why Other Options Are Wrong:

• 20, 27, 28, 18: Do not match the computed increment from 40 to the required 64 men.

Common Pitfalls:
Forgetting it asks for “more men” (M − 40), or inverting a ratio (using 25/20 instead of 20/25). Keep ratio direction consistent.

Final Answer:
24