A, B and C can finish a piece of work in 30, 40, and 60 days respectively. 10 days after they started to work together B leaves. 4 days after B left, A leaves and C completes the remaining work. Find how many days C had worked altogether.

This is how i did it: Please let me know if there is another easier way of solving it:

rate of A = 1/30

rate of B = 1/40

rate of C = 1/60

Work completed by all 3 in 10 days is W = rate * time


(1/30 + 1/40 + 1/60) * 10 = 3/4


Work left to complete = 1-3/4 = 1/4


Since B left after 10 days, the remaining work will have to be finished by A + C

rate of A + C together = (1/30 + 1/60)

Work done by A+C = (1/30 + 1/60) * 4 = 1/5

Work Left for C to complete alone = 1/4 - 1/5 = 1/20

Time required for C to complete 1/20 work alone = rate of C * time = 1/60 * time

Therefore time required for C to complete the remaining , 1/20 of the work @ 1/60 = 3 days

Total days worked by C = 10 + 4 + 3 = 17 days