A and B can complete a certain work in 12 days and 15 days, respectively. They worked together for 5 days. C alone completed the remaining work in 3 days, A and C together can complete the same work in:

6 days

Efficiency of A + B = 5 + 4 = 9

Work done in 5 days = (efficiency of A + B) x No. of days

                              = 9 x 5 = 45

Remaining work = 60 - 45 = 15 

This work is done by C alone in 3 days,

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

                             = \(\frac{15}{3}\) = 5

Efficiency of A + C = 5 + 5 = 10

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

                                                                  = \(\frac{60}{10}\) = 6 days