A can do a piece of work in 24 days and B in 40 days. They work together for 12 days and then both leave the work. Then C alone finishes the remaining work in 6 days. In how many days will C finish the full work?

30 days

                     A  :  B

Days             24 : 40  =  3 : 5

Efficiency        5 : 3

Say, the total work = 120

Work done A + B in 8 days = Efficiency x No. Of Days = (3 + 5) x 12 = 8 x 12 = 96

Remaining work = 120 - 96 = 24

This work is completed by C in 6 days,

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

                             = \(\frac{24}{6}\) = 4

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

                                                                 = \(\frac{120}{4}\) = 30 days