A can do 20% of a work in 7 days, whereas B can do one - eighth of the same work in same time. Both work together for 10 days. C completes the remaining work in 25 days. Find the time taken by A and C together to complete the work. 

20 days

Time taken by A to complete 20% of the work = 7 days

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

Time taken by B to complete one - eighth of the work = 7 days

Time taken by B to complete 100% of the work = 56 days

Total work = 280

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

                                        = (5 + 8) x 10 = 13 x 10 = 130

Work left = 280 - 130 = 150

Efficiency of C = \(\frac{Work}{Time\; taken}\)   = \(\frac{150}{25}\) = 6

Efficiency of A and C = 8 + 6 = 14

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

                                                                 = \(\frac{280}{14}\) = 20 days