If 12 men do a piece of work in 20 days, then in how many days will 60 men do the same work?

Question

Accepted Answer

To determine how many days it will take for 60 men to complete the same piece of work that 12 men can complete in 20 days, we can use the concept of man-days, which is a measure of the total amount of work done.

1. **Calculate the total amount of work in man-days:**
   - If 12 men can complete the work in 20 days, the total work is calculated as:
     $$
     \text{Total work} = 12 \text{ men} \times 20 \text{ days} = 240 \text{ man-days}
     $$

2. **Determine how many days 60 men will take to complete the same work:**
   - We know the total work required is 240 man-days. If 60 men are working, the number of days required can be calculated by dividing the total man-days by the number of men:
     $$
     \text{Number of days} = \frac{240 \text{ man-days}}{60 \text{ men}} = 4 \text{ days}
     $$

Therefore, 60 men will complete the work in 4 days, which corresponds to Option 1.

**Explanation of why other options are incorrect:**

- **Option 2 (3 days):** If 60 men were to complete the work in 3 days, the total man-days would be:
  $$
  60 \text{ men} \times 3 \text{ days} = 180 \text{ man-days}
  $$
  This is less than the required 240 man-days, so 3 days is insufficient.

- **Option 3 (2 days):** If 60 men were to complete the work in 2 days, the total man-days would be:
  $$
  60 \text{ men} \times 2 \text{ days} = 120 \text{ man-days}
  $$
  This is also less than the required 240 man-days, so 2 days is insufficient.

- **Option 4 (6 days):** If 60 men were to complete the work in 6 days, the total man-days would be:
  $$
  60 \text{ men} \times 6 \text{ days} = 360 \text{ man-days}
  $$
  This exceeds the required 240 man-days, indicating that 6 days is more than necessary.

In conclusion, the correct answer is Option 1, as 60 men will complete the work in exactly 4 days, matching the required 240 man-days.