A builder decided to build a farm house in 40 days. He employed 100 workers in the beginning and 100 more after 35 days and completed the c…

Let 100 workers would have built the farm house in x days

∴ one day’s work of 100 workers = 1/x of the total work

Now, they worked for 35 days

∴ 35/x of the work was completed

∴ work left = 1 – (35/x) = (x - 35)/x of the total work

Now, after 35 days, 100 more workers were hired.

Hence, one day’s work of 200 workers = 2/x of the total work

The 200 workers worked for 5 days to finish the farm house

∴ work done in last 5 days = 5 × one day’s work of 200 workers = 10/x of the total work

Now, work done in the last 5 days = work left after 35 days

⇒ 10/x = (x - 35)/x

⇒ x = 45 days

Hence, the 100 workers would have finished this work in 45 days and hence the contractor would have been 5 days behind schedule.