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 = ?

Answer: Option A

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
$$\begin{array}{rl}& =\left(\frac{3}{2}\times 60\right)\\ & =\text{90 days}\end{array}$$
So, A takes 30 days to do the work
$$\begin{array}{rl}& \text{A’s 1 day’s work}=\frac{1}{30}\\ & \text{B’s 1 day’s work}=\frac{1}{90}\\ & \left(\text{A}+\text{B}\right)\text{’s 1 day’s work}\\ & =\left(\frac{1}{30}+\frac{1}{90}\right)\\ & =\frac{4}{90}\\ & =\frac{2}{45}\end{array}$$
∴ A and B together can do the job in
$$\begin{array}{rl}& =\frac{45}{2}\\ & =22\frac{1}{2}\text{days}\end{array}$$