A can do \(\frac{4}{5}\)th of a work in 16 days, B can do \(\frac{1}{3}\)rd of the same work in 4 days. How much time will they take to complete double the work together? 

15 days

Time taken by A to complete \(\frac{4}{5}\) of the work = 16

Time taken  by A  to complete 100% of the work = 20

Time taken  by B to complete \(\frac{1}{3}\) of the work = 4

Time taken  by B  to complete 100% of the work = 12

Total efficiency = 3 + 5 = 8

Time taken by A and B together = \(\frac{Total\; work}{Efficiency}\)

                                               = \(\frac{60}{8}\) = 7\(\frac{1}{2}\) days

Time taken by A and B together to complete double the work = 15 days