Let's break down the problem step by step:

Given:

• Total road length = 3000 meters
• Total time to complete = 30 days
• Total men employed = 50 men
• Working hours per day initially = 8 hours
• After 20 days, only 1200 meters have been completed.
• Now, each man works 10 hours a day.

We need to determine how many additional men the contractor needs to hire to finish the road in the remaining time.

Step 1: Calculate the total work required to complete the road.

The total work needed is the remaining distance: $\text{Remaining work} = 3000 \, \text{m} - 1200 \, \text{m} = 1800 \, \text{m}$

Step 2: Determine the total work already done by the current workers in the first 20 days.

The number of men working in the first 20 days is 50, and they work 8 hours per day. The total number of man-hours spent in the first 20 days is: $\text{Man-hours in 20 days} = 50 \, \text{men} \times 8 \, \text{hours/day} \times 20 \, \text{days} = 8000 \, \text{man-hours}$

Now, since 1200 meters of road have been completed in 8000 man-hours, the number of man-hours required to complete 1 meter of road is: $\frac{8000 \, \text{man-hours}}{1200 \, \text{meters}} = 6.67 \, \text{man-hours per meter}$

Step 3: Calculate how many man-hours are required to complete the remaining 1800 meters of road.

To finish the remaining 1800 meters, the total number of man-hours required is: $\text{Man-hours required for remaining work} = 1800 \, \text{meters} \times 6.67 \, \text{man-hours per meter} = 12,000 \, \text{man-hours}$

Step 4: Calculate the remaining number of days.

Since 20 days have already passed, there are 10 days left to finish the remaining work.

Step 5: Determine how many man-hours can be completed in the remaining time.

If each man now works 10 hours per day, the total number of man-hours that can be worked by the existing 50 men in the next 10 days is: $\text{Total man-hours available} = 50 \, \text{men} \times 10 \, \text{hours/day} \times 10 \, \text{days} = 5000 \, \text{man-hours}$

Step 6: Calculate the shortfall in man-hours.

The total number of man-hours required to complete the remaining work is 12,000 man-hours, and the current team can only contribute 5000 man-hours. Therefore, the shortfall in man-hours is: $\text{Shortfall in man-hours} = 12,000 \, \text{man-hours} - 5000 \, \text{man-hours} = 7000 \, \text{man-hours}$

Step 7: Calculate the number of additional men needed.

If each new man works 10 hours per day for the remaining 10 days, each man will contribute: $10 \, \text{hours/day} \times 10 \, \text{days} = 100 \, \text{man-hours}$

Now, to cover the shortfall of 7000 man-hours, the number of additional men required is: $\frac{7000 \, \text{man-hours}}{100 \, \text{man-hours per man}} = 70 \, \text{men}$

Conclusion:

The contractor needs to employ 70 additional men to finish the work on time.

Let me know if you have further questions or need clarification!

Related Questions:

1. How can we calculate the number of man-hours required for different types of work?
2. What is the impact of changing work hours on project timelines?
3. How does increasing the number of workers affect the overall efficiency of a project?
4. How do you calculate the efficiency of a team based on their output?
5. What other factors might influence the contractor’s decision to hire more workers?

Tip:

When facing tight project deadlines, it's crucial to carefully assess both the number of workers and the amount of time remaining to ensure you can meet the goal on time.