Question

If 20 men can build a wall 66 meters long in 6 days, what length of a similar wall can be built by 86 men in 8 days?

• A. \(49 \, \text{m}\)
• B. \(59 \, \text{m}\)
• C. \(61 \, \text{m}\)
• D. \(70 \, \text{m}\)
• E.

Hint:

For work problems, use the formula: \[ \text{Work} = \text{Number of men} \times \text{Number of days}. \] This allows you to calculate the work done by varying numbers of workers and time.

Answer 1

The Correct Option is A

Step 1: Calculate the length of the wall built by 20 men in 1 day. Given that 20 men build a 66-meter wall in 6 days: \[ \text{Wall built by 20 men in 1 day} = \frac{66}{6} = 11 \text{ m}. \] Step 2: Find the length of the wall built by 1 man in 1 day: \[ \text{Wall built by 1 man in 1 day} = \frac{11}{20} = 0.55 \text{ m}. \] Step 3: Calculate the length of the wall built by 86 men in 1 day: \[ \text{Wall built by 86 men in 1 day} = 0.55 \times 86 = 47.3 \text{ m}. \] Step 4: Determine the total length of the wall built by 86 men in 8 days: \[ \text{Total wall built} = 47.3 \times 8 = 378.4 \text{ m}. \] Thus, the total length of the wall built by 86 men in 8 days is **378.4 meters**.