120 men can finish a work in 200 days. After 5-days, 30 men left the work. Now in how many days the work will be completed?
As CaptainBlack has pointed out, each man does $\displaystyle \displaystyle\frac{1}{24000}$-th of the work each day.
For 5 days, we have 120 men doing work. $\displaystyle \displaystyle120*5=600$
$\displaystyle \displaystyle\frac{600}{24000}=\frac{1}{40}$-th of the work has been done in those five days.
Now we have 90 men working. Let's assign a variable x to the number of days required to finish the work.
$\displaystyle \displaystyle90*\frac{1}{24000}=\frac{9}{2400}$ of the work is done each day with 90 men.
now we have:
$\displaystyle \displaystyle\frac{9}{2400}*x=\frac{39}{40}$ because 1/40 of the work was done in the first five days.
x=260 days.
Now we add the initial 5 days and we come to a total of 265 days.
Alternatively,
there is an inverse proportion between the number of men required
and the time taken for completion.
Similar to the concept of "man-hours", here we have "man-days".
$\displaystyle men(days)=constant$
$\displaystyle 120(200)=$ "man-days" required for completion.
$\displaystyle 120(5)+x(90)=120(200)\Rightarrow\ x(90)=120(200-5)$
$\displaystyle \displaystyle\Rightarrow\ x=\frac{120(195)}{90}$
"x" is the remaining days needed for completion.