A can do 50% of a work in 14 days, whereas B can do 60% of the same work in 21 days. Both work together for 10 days. C completes the remaining work in 5 days. Find the time taken by B and C together to complete the work. 

10 days

Time taken by A to complete 50% of the work = 14 days

Time taken by A to complete 100% of the work = 28 days 

Time taken by B to complete 60% of the work = 21 days

Time taken by B to complete 100% of the work = 35 days

Total work = 140

Work completed in 10 days = Efficiency x No. of days 

                                        = (5 + 4) x 10 = 9 x 10 = 90

Work left = 140 - 90 = 50

Efficiency of C = \(\frac{Work}{Time\; taken}\)   = \(\frac{50}{5}\) = 10

Efficiency of B and C = 4 + 10 = 14

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

                                                                 = \(\frac{140}{14}\) = 10 days