A contractor agreed to construct a 12 km road in 180 days for which he employed 120 men. After 80 days construction of only 4 km road was completed. How many additional men should he employ to complete the work as per the agreement?

To solve this problem, we need to find out how many additional men the contractor should employ to complete the remaining 8 km of the road within the agreed-upon 180 days.

First, let's calculate the rate at which the contractor and his current team are constructing the road. In 80 days, they were able to complete 4 km of the road. Therefore, their rate of construction is 4 km / 80 days = 0.05 km/day.

Now, let's calculate how many days it would take for the contractor and his current team to complete the remaining 8 km of the road. We can use the rate of construction we just calculated:

Time = Distance / Rate Time = 8 km / 0.05 km/day Time = 160 days

Since the contractor has already used up 80 days, he has 180 - 80 = 100 days left to complete the remaining 8 km of the road.

To find out how many additional men the contractor should employ, we can set up a proportion:

120 men / 80 days = X men / 100 days

Cross-multiplying, we get:

120 men * 100 days = 80 days * X men 12,000 men-days = 80X men-days

Dividing both sides by 80, we find:

12,000 men-days / 80 = X men 150 men = X men

Therefore, the contractor should employ an additional 150 men to complete the work as per the agreement.