$16$ men can finish $80$% work in $24$ days.. $16$ men can finish $80$% work in $24$ days. When should $8$ men leave the work so that the whole work is completed in $40$ days? (Answer: $20$days).
MY Attempt:
in $24$ days, $16$ men can do $\dfrac {4}{5}$ work.
In $1$ day, $16$ men can do $\dfrac {1}{30}$ work.
In $1$ day, $1$ man can do $\dfrac {1}{480}$ work.
now, what is the simplest method to complete it further?
 A: OK, with 1 man doing $\frac{1}{480}$ of the work, 480 'man-days' of work are needed. The 16 men perform 16 man-days of work per day for $x$ days, after which the 8 men get 8 'man-days' of work done for another $40-x$ days.
So: $16x + 8(40-x) =480$
Thus: $8x +320=480$
Hence: $8x=160$
Therefore: $x=20$
A: Let $t$ be the number of days when the 8 men leave. Then, the amount of work  $w(u)$ finished after working for $u$ days is given by
$$w(u)=\frac{(16-8)\cdot u}{480}+\frac{8t}{480}$$
(assuming that $u>t$). The first term corresponds to 16-8 men working all u days. The second term is the additional 8 men that work only the first $t$ days. Now, solve for $t$ in $w(40)=1$.
Edit: How to get $w(u)$: As another example, assume $p$ men work for $u$ days. As you have already pointed out, one man does $\frac{1}{480}$ of the entire work. So, if $p$ men work for $u$ days, you get done $\frac{pu}{480}$ of the work. You can write $w(u)=\frac{pu}{480}$ to make the number of days worked $u$ a variable. 
Now for my expression of $w(u)$: I've split the amount of work done into two parts, depending on the number of men working. You can assume that 16-8 men work for the entire time, i.e. $u$ days. This is the first term. In addition, in the first $t$ days 8 extra men work (which will be removed from the team after $t$ days). This corresponds to the second term.
A: As 16  men can finish 80% work in 24 days so 80 % work = 16*24 units 
so total work = 100/80 *24*16 = 480 units
work need to be completed in 40 days. 
so let after n days 8 men left the job then 
16*n + 8*(40-n) = 480
8n + 320 = 480
n = 20
so after 20 days 8 men left the job.
