A takes twice as much time as B or thrice as much time as C to complete a piece of work. Working together, the trio can complete this work in 2 days. How many days will B take to complete the work alone?

6

According to the question,

A takes twice as much time as B or thrice as much time as C to complete a piece of work, therefore,

As, Efficiency α \(\frac{1}{Time}\)

⇒               A : B : C

Efficiency    1 : 2 : 3  

⇒ A + B + C completes a work in 2 days = (1 + 2 + 3) x 2 = 12 units.  ..(Efficiency × Days = Total work) 

⇒ Time required by B to complete whole work alone = \(\frac{12}{2}\) = 6 days,        ..(\(\frac{Work}{Efficiency}\) = Time)