A is twice as efficient as B and B is thrice as efficient as C. Working together, they can finish a certain work in 5 days. If A and C worked together for 5 days then B alone would complete the remaining work in _____.

5 days

Given, 

A is twice as efficient as B and B is thrice as efficient as C, therefore,

                       A : B : C

                       2 : 1

    .                     : 3 : 1 

Efficiency          6 : 3 : 1

⇒ A + B + C can complete a work in 5 days = (6 + 3 + 1) x 10 = 50 units ..(Efficiency × Days = Total work)

⇒ A + C worked for 5 days = (6 + 1) x 5 = 35 units 

⇒ Remaining work = 50 - 35 = 15 units.

⇒ Time taken by B to complete 15 units = \(\frac{15}{3}\) = 5 days.    ..(\(\frac{Work}{Efficiency}\) = Time)