A can do a piece of work in 32 days and B can do the same work in 24 days. If they start the work and leave after 10 days and remaining work is completed by C in 13 days. How many days does C need to finish the work alone?

48 days

Total efficiency of A + B = 3 + 4 = 7

Work done by A & B in 10 days = Efficiency x No. of days = 7 x 10 = 70

Work left = 96 - 70 = 26

Efficiency of C = \(\frac{Work}{No.\; of\; days}\) = \(\frac{26}{13}\) = 2

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

                                                                 = \(\frac{96}{2}\) = 48 days