Expert: Scott A Wilson - 10/4/2009

Question
a contractor undertakes to dig a canal 6 km long in 35 days and employed 90 men.he finds that after 20 days only 2km of canal has been completed.how many more men must be employed to finish the work in time

Answer
Canal: 6 km long;
Men: 90;
Days to do it: 35.

Time passed: 20 days;
Canal built: 2km.

How many men must be employed if they work at this rate to get the job done in 35 days?

Well, 20 days have passed already, so there are 15 to go.

In 20 days, he has onle done 1/3 of the work.
This means he would need 40 days to do the other 2/3 of the work since 40 is twice 20.

However, it needs to be done in 15 days.
Since people*days=completion, we have 90 men in 40 days,
but we need to reduce the 40 to 15, so we have to multiply that by 15/40.
To gets the same completion time, we have to multiply people by 40/15.
Note that 40/15 reduces to 8/3.

We have 90 people, a thrid of them is 30.
WE already have 3/3, so 8/3 - 3/3 = 5/3, and 1/3 is 30, so 5/3 is 150.

This means that hiring 150 more people will get the job done on time.

See, 90 men would have taken 40 days, but with 150 more men, that will multiply our time to complet the job by 90/(90+150) = 9/24 = 3/8.  3/8 of 40 = 15, and that's the number of days left.