Ajit is two times as good a workman as Badrinath and therefore is able to finish a job in $30$ days less than Badrinath. Working together, they can do it in:

Let the efficiency of Badrinath be $1$.Since Ajit is twice as good, the efficiency of Ajit is $2$.The ratio of time taken to complete a job is inversely proportional to their efficiencies:
$$\text{Ratio of time taken (Ajit : Badrinath)}=1:2$$
Let the time taken by Ajit be $x$ days and Badrinath be $2x$ days.The difference in days is given as $30$:
$$2x-x=30⟹x=30\text{ days}$$
Thus:Time taken by Ajit = $30$ daysTime taken by Badrinath = $2\times 30=60$ daysTotal work can be calculated as:
$$\text{Total Work}=\text{Efficiency}\times \text{Time}=2\times 30=60\text{ units}$$
Combined efficiency of Ajit and Badrinath = $2+1=3$ units/day.Time taken working together:
$$\text{Time}=\frac{\text{Total Work}}{\text{Combined Efficiency}}=\frac{60}{3}=20\text{ days}$$