So, I have apparently forgotten entirely how I used to approach such problems. A sample statement is as follows:
24 trained workers can complete a task in 16 days, whereas 32 untrained workers do the same task in 24 days. If 16 trained and 16 untrained workers do the work together for 12 days; how many more trained workers are needed to complete the remaining work in 2 days?
Based on what I remember, I have:
Work done by trained person per day $ = \dfrac{1}{16 \cdot 24} $ and work done by untrained person per day $ = \dfrac{1}{24 \cdot 32} $. Since 16 each of them work together, they can complete the whole work in $ 16 $ days.
And this is where I get stuck. Now they have 4 days worth of work remaining. What should I do now?
$16$ trained workers working for 12 days do $16\cdot \frac 1{16\cdot24}\cdot 12 = 1/2$ of work.
$16$ untrained do $16\cdot\frac 1{24\cdot32}\cdot 12=1/4$ in the same time.
So the team does $3/4$ of work in $12$ days.
For the remaining $1/4$ to be completed in $2$ days you need additional $n$ untrained workes which satisfies:
'work done by 16 trained and (16+n) untrained in 2 days = 1/4'.