A can do 33.33% of a work in 10 days, and B can do 20% of the same work in 9 days. They worked together for 8 days. C alone completed 30% of the remaining work in 10 days. A and C together can do the same work in

A does 33.33% (1/3) of work in 10 days, so total work in 30 days. A's rate = 1/30 work/day. B does 20% (1/5) of work in 9 days, so total work in 45 days. B's rate = 1/45 work/day. Work done by A and B together in 8 days = 8(1/30 + 1/45) = 8(3/90 + 2/90) = 8(5/90) = 40/90 = 4/9 of work. Remaining = 5/9. C does 30% of remaining (5/9) in 10 days, so C does 0.3 × 5/9 = 1/6 of total work in 10 days. C's rate = 1/60 work/day. A and C together: 1/30 + 1/60 = 3/60 = 1/20 work/day, so they complete the work in 20 days.