6 men and 1 woman can complete some work in 2 days.3 men and 8 women

6M + 1W can finish a work in 2 days.

3M + 8W can finish a work in 1 day.

Therefore, 3M + 8W can finish 2 work in 2 days.

Thus, combined work of (6M+1W)+(3M+8W) in 2 days is 1+2 or 3 works.
That is, 9M+9W can finish 3 works in 2 days OR 1M and 1W can finish 3 works in 2*9 days.

Finally, 1M + 1W can finish 1 work in \(\frac{18}{3}\) or 6 days.


C


OR

6M + 1W can finish a work in 2 days or, 12M + 2W can finish a work in one day.

3M + 8W can finish a work in 1 day.

Thus, \(12M+2W=3M+8W……..9M=6W……3M=2W\)
This means 3M+8W=2W+8W=10W can finish a work in 1 day. But we are looking for 1M+1W or \(\frac{2W}{3}+1=\frac{5W}{3}\).

10W in 1day means 1W in 10 days.
Therefore, \(\frac{5W}{3}\) in \(\frac{10}{\frac{5W}{3}}=\frac{10*3}{5}=6\) days.