Work–men–days (direct proportion): If 20 men can build a similar wall 56 meters long in 6 days, what length of such a wall can 35 men build in 3 days?

Introduction / Context:This is a classic unitary-method (work–time) question. For similar work, total output is directly proportional to the product men * days, assuming all men work at the same constant rate. We use this proportionality to scale from one scenario to another.Given Data / Assumptions:

• 20 men in 6 days build 56 meters of wall.
• We need the length built by 35 men in 3 days (same wall type and productivity per man).
• Rates are constant and additive across workers.

Concept / Approach:Total work (length of wall) ∝ men * days. Hence, length2 = length1 * (men2 * days2) / (men1 * days1). Compute once and select the matching option.Step-by-Step Solution:

Verification / Alternative check:Use direct ratio: length2 = 56 * (35*3)/(20*6) = 56 * 105 / 120 = 56 * 0.875 = 49 m. Same result via either method.Why Other Options Are Wrong:

• 40, 43, 48: All underestimate the proportional increase from 120 to 105 man-days relative to the 56 m benchmark; only 49 fits the precise scaling.

Common Pitfalls:Dividing by the wrong base (e.g., scaling by men only and forgetting days) or assuming inverse proportion. Here, output grows with both men and days.

Final Answer: