A and B can complete a certain work in 13 days and 26 days, respectively. They worked together for 4 days. C alone completed the remaining work in  7 days, A, B and C together can complete the same work in:

5\(\frac{1}{5}\) days

Efficiency of A + B = 2 + 1 = 3

Work done in 4 days = (efficiency of A + B) x No. of days

                              = 3 x 4 = 12

Remaining work = 26 - 12 = 14

This work is done by C alone in 7 days,

Then efficiency of C = \(\frac{work\; done}{no.\; of\; days}\)

                             = \(\frac{14}{7}\) = 2

Efficiency of A + B   +  C = 2 + 1 + 2 = 5

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

                                                                  = \(\frac{26}{5}\) = 5\(\frac{1}{5}\) days