A is twice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B. In how many days they can complete the whole work; working together?

Efficiency → $\stackrel{A :}{2} : \stackrel{B}{1}$
Time $\to 1:2\left(\because \text{ Efficiency }\propto \frac{1}{\text{ Time }}\right)$
Difference →30 days
A will complete the work =30 days
B will complete the work =60 days
Let total work is 60 units (LCM of 30,60 )
Whole work will be completed, working together
$=\frac{60}{2+1}$[ efficency ]=20 days