We can solve this using the concept of work done, which is inversely proportional to the number of men, assuming all men work at the same rate.

Given:

• 100 men can complete the work in 20 days.
• We need to find out how many days 125 men will take to do the same work.

Let's assume the total work is $W$.

The formula to calculate work is: $\text{Work} = \text{Men} \times \text{Days}$ For 100 men working for 20 days, the total work $W$ is: $W = 100 \times 20 = 2000 \text{ man-days}$ Now, if 125 men are working, the number of days $D$ they will take to complete the same work $W$ is: $W = 125 \times D$ Since the total work is 2000 man-days, we can equate: $125 \times D = 2000$ Solving for $D$: $D = \frac{2000}{125} = 16 \text{ days}$

Therefore, 125 men can complete the work in 16 days.

Would you like further clarification or additional details?

Here are 5 related questions for you:

1. How would the time change if 150 men worked on the same task?
2. What if only 80 men were available? How many days would it take them?
3. Can we model this as a proportion problem instead of using man-days?
4. What happens if the work increases by 50%? How many days would 125 men take then?
5. How does the efficiency of men working in a team affect this calculation?

Tip: When solving these types of work problems, the key is to keep the total work (man-days) constant across different scenarios.