A and B together can complete a work in 60 minutes, while B and C take 30 minutes and C and A in 40 minutes. Find the time taken by A, B and C to complete the same work.

26.67 minutes

Efficiency of A + B + C = \(\frac{1}{2}\) ((A + B) + (B + C) (C + A))

                                 = \(\frac{1}{2}\)  (2 + 4 + 3) = \(\frac{9}{2}\) 

Time taken by (A+ B + C) = \(\frac{Total\; work}{Efficiency}\)

                                       = \(\frac{120\; \times \; 2}{9}\) = 26.67 minutes