A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

It is said that the Entire work (W) is finished in 40 days .
First 35 days : 100 men worked .
Next 5 days : (100+100) men worked.

Let the amount of work done by each men per day be "K"
So, 100(K)(35) + 200(K)(5) = W 
So, K = $$\dfrac{\ W}{4500}$$

If he had not engaged additional men, then only 100 people would have only worked with efficiency "K" till the entire work is finished. So lets time taken to finish the work in this case be "T" : 
                            100(K)(T) = W 
                             T  =$$\dfrac{\ W}{100\left(K\right)}$$
                                 = 4500/100 
                                 = 45 days.

Therefore, the work could have been finished with a delay of (45-40) days = 5 days.