$1$ man or $2$ women can finish the work in $20$ days.

Work by $1$ man in $1$ day $= \dfrac{1}{20}$
Work by $1$ woman in $1$ day $= \dfrac{1}{40}$

For $3$ men and $1$ woman:
Total work per day $= 3 \times \dfrac{1}{20} + 1 \times \dfrac{1}{40}$
$= \dfrac{6}{40} + \dfrac{1}{40} = \dfrac{7}{40}$

Time to finish the job $= \dfrac{1}{(7/40)} = \dfrac{40}{7}$ days
$\approx 5.71$ days

✅ Final Answer: $ \dfrac{40}{7} $ days