correct answer is: c) 25 days

Explanation

3 men = 5 women
\therefore 1 men =\large\frac{5}{3} women
\therefore 6 men =\large\left(\frac{5\times6}{3}\right) women
\rightarrow 10 women
And, 12 men =\large\left(\frac{5\times12}{3}\right) women
\rightarrow 20 women.
So that,
6 men and 2 women equal to:
\left(10+2\right)=12 women.
And, 12 men and 4 women equal to:
\left(20+4\right)=24 women.

Now,
12 women can finish a work in 50 days
\therefore 1 women can finish a work =\left(50\times12\right) days
\therefore 24 women can finish a work in =\large\left(\frac{50\times12}{24}\right) days
\rightarrow 25 days.
Ans: 12 men and 4 women will take 25 days to finish the work.

Another way, Rules of Three Method

Women and Days are Inversely Proportional.
\therefore\;24\;:\;12\;:\;:\;50\;:\;x
\rightarrow\large\frac{24}{12}=\frac{50}{x}
\rightarrow 24x=50\times12
\rightarrow x=\large\frac{50\times12}{24}
\rightarrow x=25
Ans: It will take 25 days to finish the work.

Other variants of this particular math question are:

1. How many days will it take for 12 men and 4 women to complete a task if 6 men and 2 women typically finish it in 50 days, and the work output of 3 men equals that of 5 women?
2. If the work output of 3 men equals that of 5 women, and 6 men along with 2 women can complete a task in 50 days, how many days will it take for 12 men and 4 women to finish the same task?
3. Given that 6 men and 2 women can complete a task in 50 days, and the work of 3 men equals that of 5 women, how long will it take for 12 men and 4 women to complete the same task?
4. Suppose a task normally requires 6 men and 2 women to complete in 50 days, and the work output of 3 men equals that of 5 women. How long will it take for 12 men and 4 women to finish the task?