A can do one - third of a work in 9 days, whereas B can do 25% of the same work in same no. of days. Both work together for 12 days. C completes the remaining work in 4 days. Find the time taken by B and C together to complete the work. 

12 days

Time taken by A to complete one - third of the work = 9 days

Time taken by A to complete 100% of the work = 27 days 

Time taken by B to complete 25% of the work = 9 days

Time taken by B to complete 100% of the work = 36 days

Total work = 108

Work completed in 12 days = Efficiency x No. of days 

                                        = (3 + 4) x 12 = 7 x 12 = 84

Work left = 108 - 74 = 24

Efficiency of C = \(\frac{Work}{Time\; taken}\)   = \(\frac{24}{4}\) = 6

Efficiency of B and C = 3 + 6 = 9

Time taken by B and C to complete the work = \(\frac{Total\; work}{Efficiency}\)

                                                                 = \(\frac{108}{9}\) = 12 days