Pranjal takes twice as much time as Vikram or thrice as much time as Ashwin to finish a piece of work. Working together, they can finish the work in 6 days. Vikram can do the work alone in:

18 days

According to the question,

Pranjal takes twice as much time as Vikram or thrice as much time as Ashwin to finish a piece of work.

Efficiency α \(\frac{1}{Time}\)

Therefore,

                 Pranjal : Vikram : Ashwin

Efficiency      1      :     2      :    3

⇒ All of them working together can complete the work in 6 days = (1+2+3) x 6 = 6 x 6 = 36 units,      ..(Efficiency × Days = Total work) 

⇒ Time required for Vikram to complete the work alone = \(\frac{36}{2}\) = 18 days,       ..(\(\frac{Work}{Efficiency}\) = Time)