4 men and 4 women can complete a work in 5 days, while 2 men and 5 women can finish it in 6 days. How much time (in days) will be taken by 1 woman working alone and 1 man working all by himself to complete the work, respectively?

Let the work rate of a man be M and a woman be W.
From the given information, total work is equal in both cases:

Work=(4M+4W)×5=(2M+5W)×6
20M+20W=12M+30W
20M−12M=30W−20W
8M=10W⟹4M=5W⟹M=
4
5
​
W
Now substitute M into the total work equation:

Total Work=(4(
4
5
​
W)+4W)×5=(5W+4W)×5=9W×5=45W
Time taken by 1 woman working alone:

Time
W
​
=
1W
45W
​
=45 days
Time taken by 1 man working alone:

Time
M
​
=
M
45W
​
=
4
5
​
W
45W
​
=45×
5
4
​
=36 days
Thus, the times taken are 45 and 36 days respectively.