A can do a piece of work in 18 days and B can do it in 15 days. They work together for 4 days, then B leaves and A alone continues. 5 days later C joins and the work is completed in 3 more days. In how many days can C do the work alone?

45 days   

Work done by A and B together in 4 days = efficiency x no. of days = 11 x 4 = 44

Work left after this = 90 - 44 = 46

This work is continues by A alone in the next 5 days,

With efficiency of 5, work done by A = 5 x 5 = 25 

Work lefty thereafter, 46 - 25 = 21

This is completed by A and C in 3 days, 

then efficiency of A and C together = \(\frac{work}{no.\; of\;\; days}\) 

                                                   =\(\frac{21}{3}\) = 7

Efficiency of C = 7 - 5 = 2

Time taken C alone to do the total work = \(\frac{Total\; work }{efficiency}\)

                                                          = \(\frac{90}{2}\) = 45 days