a) 15 days

b) 20 days

c) 25 days

d) 30 days

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:

**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?****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?****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?****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?**