A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

Explanation:-

$$\eqalign{ & {\text{Ration}}\,{\text{of}}\,{\text{rates}}\,{\text{of}}\,{\text{working}}\,{\text{of}}\,{\text{A}}\,{\text{and}}\,{\text{B}} \cr & = 2:1 \cr & {\text{So,}}\,{\text{ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}} = 1:2 \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{12}} \cr & \therefore {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{3};\,({\text{2times}}\,{\text{of}}\,{\text{B's}}\,{\text{work}}) \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{6} + \frac{1}{{12}}} \right) = \frac{3}{{12}} = \frac{1}{4} \cr & {\text{So,}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{together}}\,{\text{can}}\,{\text{finish}}\,{\text{the}} \cr & {\text{work}}\,{\text{in}}\,{\text{4}}\,{\text{days}}{\text{.}}\, \cr}$$