To do a certain work, the ratio of the efficiencies of A, B and C is 5 : 7 : 8. Working together, they can complete the same work in 29 days. A and B work together for 45 days. The remaining work will be completed by C alone in:

5 days

                A   :   B   :   C

Efficiency   5   :   7   :    8

(A + B + C) can complete  a work in 29 days.

Hence, the total work = 29 (A + B + C) = 29 (5 + 7 + 8) = 580

(A + B) worked for 45 days = (5 + 7) × 45 = 540

Remaining work = 580 - 540 = 40

C can complete the remaining work = \(\frac{40}{8}\) = 5 days