Question

Time
SA contractor undertook to build a road in 180 days. He employed 150 men for the construction of
road. After 60 days, he found that only one-fourth of road could be built. How many additional men
should be employed to complete the work in time?
d. Find the product (- xy + bk) (xy +bk)
(2)​

Answer 1

Answer:

The contractor will need 75 additional men

Step-by-step explanation:

150 men worked for 60 days and completed 1/4 of the road

Let the work done by 1 man in 1 day be denoted as "manday"

=> 150 men working for 60 days is (150*60) mandays = 9000 mandays

=> It took 9000 mandays to complete 1/4 of the road

=> It will take 9000*4 mandays to complete the full work

=> It will take 36000 mandays to complete the full work

=> The work is worth 36000 mandays

Now, up to the 60th day, 1/4 of the work is completed

=> 3/4 of the work is remaining

The contractor has undertaken to complete the work in 180 days.

With 60 days gone, he has 120 days left with him.

=> Time available for remaining work is 120 days

=> The contractor has 120 days to complete 3/4 of the work

The entire work is worth 36000 mandays

=> 3/4 of the work is (3/4)*36000 mandays

=> 3/4 of the work is 27000 mandays

=> 27000 mandays of work has to be completed in 120 days

Now, mandays = No. of men * No. of days

Let the number of men required for this be "m"

=> m * 120 = 27000

=> m =  225

The contractor will need a total of 225 men on the job.

As the contractor already has 150 men, he will need to deploy 75 additional men.

(Remember: 1 man works for 1 day and does 1 manday of work. Try and get the "worth" of any work in terms of "mandays")