A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

6 days

Ratio of time taken by A to B to complete the work = 2 : 1

Ratio of efficiency A to B = 1 : 2

Ratio of time taken by A to C to complete the work = 3 : 1

Ratio of efficiency A to C = 1 : 3

Overall ratio of efficiency of A , B & C = 1 : 2 : 3

As, They together complete the work in 2 days .

So, Complete work = Efficiency × Number of day

= ( 1 + 2 + 3 )R × 2

= 12R

Time taken by B alone to do the work = \(\frac{12R}{2R}\) = 6 days