A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

Explanation:-

$$\eqalign{ & {\text{Ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B = 1:3}} \cr & {\text{The}}\,{\text{time}}\,{\text{difference}}\,{\text{is}}\,\left( {{\text{3 - 1}}} \right)\,{\text{2}}\,{\text{days}} \cr & {\text{while}}\,{\text{B}}\,{\text{take}}\,{\text{3}}\,{\text{days}}\,{\text{and}}\,{\text{A}}\,{\text{takes}}\,{\text{1}}\,{\text{day}}{\text{.}} \cr & {\text{If}}\,{\text{difference}}\,{\text{of}}\,{\text{time}}\,{\text{is}}\,{\text{2}}\,{\text{days,}}\,{\text{B}}\,{\text{takes}}\,{\text{3}}\,{\text{days}}{\text{.}} \cr & {\text{If}}\,{\text{difference}}\,{\text{of}}\,{\text{time}}\,{\text{is}}\,{\text{60}}\,{\text{days,}} \cr & {\text{B}}\,{\text{takes}}\,\left( {\frac{3}{2} \times 60} \right) = 90\,{\text{days}} \cr & {\text{So,}}\,{\text{A}}\,{\text{takes}}\,{\text{30}}\,{\text{days}}\,{\text{to}}\,{\text{do}}\,{\text{the}}\,{\text{work}}{\text{.}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{30}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{90}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{{30}} + \frac{1}{{90}}} \right) = \frac{4}{{90}} = \frac{2}{{45}} \cr & \therefore {\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{together}}\,{\text{can}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\, \cr & \frac{{45}}{2} = 22\frac{1}{2}\,{\text{days}}\, \cr}$$