A is thrice as good a workman as B and so takes 60 days less than B for doing a job. The time in which they can do the job together is = ?

Solution(By Examveda Team)

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