a contractor undertakes to dig a canal of 120km long in 300 days and employs 45 men. after 200 days he finds that only 45 km of the canal has been completed, find the number of extra men whose efficiency is 25% less than previous one to be completed to finish the work on time.
Answers
45 men can dig 120 km in 300 days
Find the distance 45 men can dig in a day:
1 day = 120 ÷ 300 = 2/5 km
Find the distance 1 man can dig in a day:
45 men = 2/5 km
1 man = 2/5 ÷ 45 = 2/225 km
Find the distance 1 men with 25% less efficiency can dig:
Originally, 1 man = 2/225 km
1 man with 25% less efficiency = (100 - 25)% x 2/225 km
1 man with 25% less efficiency = 75% x 2/225 km
1 man with 25% less efficiency = 75/100 x 2/225 km
1 man with 25% less efficiency = 1/150 km
Find the amount of time left to work:
Amount of time left = 300 - 200 = 100 days
Find the amount of work 1 man can do in 100 days:
1 day = 1/150 km
100 days = 1/150 x 100 = 2/3 km
Find the amount of work left to be done:
Work left = 120 - 45 = 75 km
Find the number of men needed:
1 man = 2/3 km
Total work = 75 km
Number of men = 75 ÷ 2/3 = 112.5 ≈ 113
Answer: 113 more workers are needed to complete the work in time