36 men can build a wall 140 m long in 21 days, in how many days would 15 men be able to construct a similar wall 50 m long?

Question

Accepted Answer

To determine how many days 15 men would take to construct a similar wall 50 meters long, we can use the concept of work and manpower. Here's a detailed explanation supporting Option 4 as the correct answer:

### Explanation:

1. **Initial Work Calculation:**
   - 36 men can build a 140-meter wall in 21 days.
   - Total work required to build the wall = Number of men × Number of days = 36 men × 21 days = 756 man-days for 140 meters.

2. **Work per Meter:**
   - Work required per meter of wall = Total work / Length of wall = 756 man-days / 140 meters = 5.4 man-days per meter.

3. **Work for 50 Meters:**
   - Work required for a 50-meter wall = 5.4 man-days/meter × 50 meters = 270 man-days.

4. **Time Calculation for 15 Men:**
   - If 15 men are working, the number of days required = Total work / Number of men = 270 man-days / 15 men = 18 days.

Thus, 15 men would take 18 days to construct a 50-meter wall, which corresponds to Option 4.

### Explanation of Incorrect Options:

- **Option 1 (20 days):** 
  - If 15 men were to complete the work in 20 days, the total work done would be 15 men × 20 days = 300 man-days, which is more than the required 270 man-days. Therefore, this option is incorrect.

- **Option 2 (22 days):**
  - If 15 men were to complete the work in 22 days, the total work done would be 15 men × 22 days = 330 man-days, which exceeds the required 270 man-days. Hence, this option is incorrect.

- **Option 3 (22.5 days):**
  - If 15 men were to complete the work in 22.5 days, the total work done would be 15 men × 22.5 days = 337.5 man-days, which is significantly more than the required 270 man-days. Therefore, this option is incorrect.

In conclusion, the correct answer is Option 4, as it accurately reflects the number of days required for 15 men to construct a 50-meter wall based on the given conditions.