A can complete four - ninths of a work in 12 days and B can complete five - sixths of the same work in 45 days. They worked together for 18 days and then A left. How much time will B working alone, take to complete the remaining work?

9 days

If A completes four - ninths of the work in 12 days, 

Then time taken to complete the total work = 27 days (Apply Unitary Method)

Similarly, 

If B completes five - sixths of the work in 45 days, 

Then time taken to complete the total work = 54 days

Total work = 108 

Work completed in 18 days = Efficiency x No. Of Days = (3 + 2) x 18 = 5 x 18 = 90

Work left = 108 - 90 = 18

This work will be done by B alone in = \(\frac{18}{2}\) = 9 days