A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

Question: A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?Solution:2(A + B + C)'s 1 day's work = (1/30 + 1/24 + 1/20) = 15/120 = 1/8Therefore, (A + B + C)'s 1 day's work = 1/(2 × 8) = 1/16Work done by A, B, C in 10 days = 10/16 = 5/8Remaining work = (1 - 5/8) = 3/8A's 1 day's work = (1/16 - 1/24) = 1/48So,3/8 work will be done by A in 48 × (3/8) days = 18 days.