A and B can complete a work in 30 days while B and C can complete this work in 24 days and C and A in 20 days. They all start the work together but B and C leave the work after few days and the remaining work is completed in 18 days. Find after how many days B and C left the work?

Let A, B, C be the daily work rates. A+B = 1/30, B+C = 1/24, C+A = 1/20. Adding all: 2(A+B+C) = 1/30+1/24+1/20 = 4/120+5/120+6/120 = 15/120 = 1/8, so A+B+C = 1/16. Let d be days B and C worked. Work done by all three: d/16. Remaining work: 1 - d/16 = (16-d)/16, done by A alone in 18 days. A's rate = (A+B+C) - (B+C) = 1/16 - 1/24 = (3-2)/48 = 1/48. So (16-d)/16 = 18/48 = 3/8, giving 16-d = 6, so d = 10 days.