Answer:
Since the contractor already has 50 men, he needs to employ an additional 71 men to complete the project on time.
Explanation:
Let's first find the total amount of work needed to be done, using the given information that the road is 3000 m long:
Total amount of work = 3000 m
We know that 50 men are employed and they work 8 hours per day. So the total man-hours worked in 20 days can be calculated as:
Total man-hours worked in 20 days = 50 men x 8 hours/day x 20 days = 8000 man-hours
We also know that only 1200 m of the road is completed in 20 days. So the amount of work remaining can be calculated as:
Remaining amount of work = Total amount of work - Completed work
Remaining amount of work = 3000 m - 1200 m = 1800 m
Now, we can calculate the total number of man-hours required to complete the remaining work:
Total man-hours required = Remaining amount of work / Productivity rate
Productivity rate = (8000 man-hours) / (1200 m) = 6.67 man-hours/m
Total man-hours required = (1800 m) x (6.67 man-hours/m) = 12,006 man-hours
To complete the remaining work in 10 days, each man needs to work 10 hours per day. Therefore, the total number of men required can be calculated as:
Total men required = Total man-hours required / (Hours per day x Days available)
Total men required = 12,006 man-hours / (10 hours/day x 10 days)
Total men required = 120.06
Rounding up to the nearest whole number, the contractor needs to employ 121 men.