A can do a piece of work in 20 days and B in 30 days. They work together for 8 days and then both leave the work. Then C alone finishes the remaining work in 5 days. In how many days will C finish the full work?

15 days

                     A  :  B

Days             20 : 30

Efficiency        3 : 2

Say, the total work = 60

Work done A + B in 8 days = Efficiency x No. Of Days = (3 + 2) x 8 = 5 x 8 = 40

Remaining work = 60 - 40 = 20

This work is completed by C in 5 days,

Thus efficiency of C = \(\frac{Work}{Days}\)                          

                             = \(\frac{20}{5}\) = 4

Time taken By C alone to complete this work = \(\frac{Total\; work}{Efficiency}\)             

                                                                 = \(\frac{60}{4}\) = 15 days