A and B together can do a piece of work in 30 days, B and C together can do it in 20 days. A starts the work and works on it for 5 days, then B takes it up and works for 15 days. Finally, C finishes the work in 18 days. In how many days can C do the work when doing it separately (in days)?

Solution

(A + B)’s 1 day work = 1/30 And (B + C)’s 1 day work = 1/20 Also, A’s 5 days w + B’s 15 days w + C’s 18 days w = 1 work ⇒ A’s 5 days w + B’s 5 days w + B’s 10 days w + C’s 10 day w + C’s 8 day w = 1 work ⇒ (A + B)’s 5 days w + (B + C)’s 10 days w + C’s 8 days work = 1 work ⇒ 5/30 + 10/20 + C’s 8 days work = 1 work ⇒ 1/6 + 1/2 + C’s 8 days work = 1 work ⇒ C’s 8 days work = 1 – ( 1/6 + 1/2 ) work ⇒ C’s 8 days work = 1 – ((1 + 3)/6) = 1 - 4/6 = 1 - 2/3 ∴ C’s 8 days w = 1/3 work ∴ C will complete the work in 8 × 3 = 24 days