A is thrice as productive as C. Together they can complete a job in 22.5 days. If B joins them after they have worked for 15 days then in how many days can they finish the rest of the job if B alone can do the job in 15 days?

Let the work done by C be x units/day 
Therefore work done by A will be 3x units/day
Now therefore total work per day = 4x units
Now total work done = 22.5(4x) =90x units/day
Now B alone does the work in 15 days
so B's per day work = 6x units/ day
Now for 15 days A and C worked
so work completed in 15 days = 60x
Now remaining work = 30x
Now time taken by A,B,C together to complete 30x units of work :
30x/10x = 3 days