If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?

Options

A. A) 710 acres
B. B) 760 acres
C. C) 810 acres
D. D) 860 acres

Answer

To solve the problem, we can use the concept of man-days, which is the total amount of work done by a certain number of men over a certain number of days.

### Step-by-Step Solution:

**Step 1: Calculate the total man-days for the initial scenario.**
- We know that 12 men can reap 120 acres in 36 days.
- Total man-days = Number of men × Number of days = 12 men × 36 days = 432 man-days.

**Step 2: Determine how many acres can be reaped per man-day.**
- If 12 men can reap 120 acres in 432 man-days, then:
\[ \text{Acres per man-day} = \frac{120 \text{ acres}}{432 \text{ man-days}} = \frac{10}{36} \text{ acres/man-day} = \frac{5}{18} \text{ acres/man-day}. \]

**Step 3: Calculate the total man-days for the new scenario with 54 men and 54 days.**
- Total man-days = Number of men × Number of days = 54 men × 54 days = 2916 man-days.

**Step 4: Calculate the total acres that can be reaped by 54 men in 54 days.**
- Using the acres per man-day calculated in Step 2:
\[ \text{Total acres} = \text{Acres per man-day} × \text{Total man-days} = \frac{5}{18} \text{ acres/man-day} × 2916 \text{ man-days}. \]
- Performing the multiplication:
\[ \text{Total acres} = \frac{5 × 2916}{18} = \frac{14580}{18} = 810 \text{ acres}. \]

### Final Answer:
54 men can reap **810 acres** of land in 54 days.