A and B can complete a certain work in 27 days and 45 days, respectively. They worked together for 10 days. C alone completed the remaining work in 5 days, A and C together can complete \(\frac{7}{15}\)th of the same work in:

4.5 days

Efficiency of A + B = 5 + 3 = 8

Work done in 10 days = (efficiency of A + B) x No. of days

                                = 8 x 10 = 80

Remaining work = 135 - 80 = 55

This work is done by C alone in 5 days,

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

                             = \(\frac{55}{5}\) = 11

Efficiency of A + C = 3 + 11 = 14

Time taken by A and C to complete \(\frac{7}{15}\)th of the work = \(\frac{Total \; work}{efficiency}\) x \(\frac{7}{15}\)

                                                                  = \(\frac{135}{14}\) x \(\frac{7}{15}\) = 4.5 days