Final answer:
A's work rate is 1/90 work per day, B's is 1/60 per day, and C's is 1/18 per day. Working together, their combined rate is 1/90 + 1/60 + 1/18 = 1/15 work per day. Hence, A, B, and C together can complete the work in 15 days.
Step-by-step explanation:
We are given that A can do 1/3 of the work in 30 days, which means A can complete the entire work in 90 days. B can do 2/5 of the work in 24 days, which means B can complete the entire work in 60 days (since 24 days is 2/5 of the time B needs to finish the work).
To find out the rates of A and B, we take the reciprocals of these times. A's rate is 1/90 work per day and B's rate is 1/60 work per day. When they work together, their combined rate is 1/90 + 1/60 = 1/36 work per day.
A and B together worked for 20 days, hence they completed 20/36 of the work. So, 16/36 (or 4/9) of the work remains. C completes this in 8 days, meaning C's rate is (4/9) / 8 = 1/18 work per day.
To find out how long it would take for all three, A, B, and C, to complete the work together, we sum their rates: 1/90 + 1/60 + 1/18 = 1/15 work per day. Therefore, working together, they will complete the work in 15 days.
The answer is A. 15 days.