A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Given:

Total length of the road = 6 km

Time allowed = 200 days

Number of persons initially employed = 140

Road completed in 60 days = 1.5 km

Concept Used:

Calculate the required number of persons to complete the remaining work in the remaining time.

Calculation:

Total work to be done = 6 km

Work completed in 60 days = 1.5 km

Remaining work = 6 km - 1.5 km = 4.5 km

Remaining time = 200 days - 60 days = 140 days

Current work rate with 140 persons:

⇒ Work rate = 1.5 km / 60 days = 0.025 km per day

⇒ Work rate per person = 0.025 km / 140 persons = 0.0001786 km per person per day

Required work rate to complete 4.5 km in 140 days:

⇒ Required work rate = 4.5 km / 140 days = 0.03214 km per day

Number of persons required = Required work rate / Work rate per person

⇒ Number of persons required = 0.03214 km / 0.0001786 km per person per day

⇒ Number of persons required ≈ 180

Additional persons needed = 180 - 140 = 40

∴ The contractor would need to employ 40 additional persons.