A can complete one - sixth of a work in 3 days and B can complete one - third of the same work in 15 days. They worked together for 8 days and then A left. How much time will B working alone, take to complete the remaining work?

17 days

If A completes one - sixth of the work in 3 days, 

Then time taken to complete the total work = 18 days (Apply Unitary Method)

Similarly, 

If B completes one - third of the work in 15 days, 

Then time taken to complete the total work = 45 days

Total work = 90

Work completed in 8 days = Efficiency x No. Of Days = (2 + 5) x 8 = 7 x 8 = 56

Work left = 90 - 56 = 34

This work will be done by B alone in = \(\frac{34}{2}\) = 17 days