Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes  \(\left(\frac{3}{2}\times60\right)\) = 90 days.

So, A takes 30 days to do the work.

A's 1 day's work = \(\frac{1}{30}\)

B's 1 day's work = \(\frac{1}{90}\)

(A + B)'s 1 day's work =  \(\left(\frac{1}{30}+\frac{1}{90}\right)=\frac{4}{90}=\frac{2}{45}.\)

A and B together can do the work in \(\frac{45}{2}=22\frac{1}{2}days\)