A can do a piece of work in 15 days and B can do it in 21 days. They work together for 5 days, then B leaves and A alone continues. 3 days later C joins and the work is completed in 2 more days. In how many days can C do the work alone?

21 days  

Work done by A and B together in 5 days = efficiency x no. of days = 12 x 5 = 60

Work left after this = 105 - 60 = 45

This work is continues by A alone in the next 3 days,

With efficiency of 7, work done by A = 7 x 3 = 21 

Work lefty thereafter, 45 - 21 = 24

This is completed by A and C in 2 days, 

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

                                                   =\(\frac{24}{2}\) = 12

Efficiency of C = 12 - 7 = 5

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

                                                          = \(\frac{105}{5}\) = 21 days