correct answer is: a) 25 days

Explanation

Here,
8 men = 12 boys
\therefore 1 men =\large\frac{12}{8} women
\therefore 24 men =\large\left(\frac{12\times24}{8}\right) boys
\rightarrow 36 boys
According to the question,
24 men and 12 boys finish the work.
Or, \left(36+12\right)=48 boys finish the work.
Now,
12 boys can finish a work in 100 days
\therefore 1 boys can finish the work in =\left(100\times12\right) days
\therefore 48 boys can finish the work in =\large\left(\frac{100\times12}{48}\right) days
\rightarrow 25 days.
Ans: 24 men and 12 boys finish the work in 25 days.

Another method to articulate this particular math query is available:

1. If either 8 men or 12 boys can complete a task in 100 days, how many days will it take for a team consisting of 24 men and 12 boys to finish the same task?
2. How many days will it take for a group comprising 24 men and 12 boys to complete a task if it normally takes either 8 men or 12 boys 100 days to finish it?
3. Given that a task can be completed by either 8 men or 12 boys in 100 days, how many days will it take for a team consisting of 24 men and 12 boys to finish the task?
4. If a task requires either 8 men or 12 boys 100 days to complete, how long will it take for a team comprising 24 men and 12 boys to finish the same task?
5. Suppose a task is typically completed by either 8 men or 12 boys in 100 days. How many days will it take for a team consisting of 24 men and 12 boys to complete the task?