If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days?

Question

If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days?

1. A. 53 m
2. B. 49 m (Correct answer)
3. C. 64 m
4. D. 43 m

Correct Answer

Option B — 49 m

Detailed Solution & Explanation

The correct answer is 49 m.

Key Points

• Wall length varies directly with both the number of men and the number of days.
• Using the chain rule: new length = 56 × (35 ÷ 20) × (3 ÷ 6).
• 35 ÷ 20 = 1.75 and 3 ÷ 6 = 0.5, so the factor is 0.875.
• New length = 56 × 0.875 = 49 metres.

Additional Information

• The standard formula for such problems is:

(M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

where M is men, D is days and W is the work done.

• Identify the direction of each relationship before computing: work rises with more men and with more days, so both factors enter as direct proportions here.
• The word *similar* in the question matters — it guarantees the second wall is of the same construction, so length alone measures the work.