A can do a piece of work in 30 days and B in 12 days. They work together for 5 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work?

24 days

                     A  :  B

Days             30 : 12   =  2 : 5

Efficiency        5 : 2

Say, the total work = 60

Work done A + B in 8 days = Efficiency x No. Of Days = (2 + 5) x 5 = 7 x 5 = 35

Remaining work = 60 - 35 = 25

This work is completed by C in 10 days,

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

                             = \(\frac{25}{10}\) = 2.5

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

                                                                 = \(\frac{60}{2.5}\) = 24 days