Ramos, Karen and Vincent take a contract to do a piece of work. Ramos can do it alone in 10 days. Karen can do it in 20 days and Vincent can do it in 40 days. They work alternately. On the 1^st day, Ramos will do it alone, on the 2^nd day, Karen will do it and on the 3^rd day, Vincent will do it alone, and so on till the work is completed. Find the time taken to complete the work.

Ramos (R) = 1/10, Karen (K) = 1/20, Vincent (V) = 1/40. Work per 3-day cycle = 4/40 + 2/40 + 1/40 = 7/40. After 4 cycles (12 days), work done = 28/40. Remaining = 12/40. Day 13: R does 4/40 (total 32/40). Day 14: K does 2/40 (total 34/40). Day 15: V does 1/40 (total 35/40). Remaining 5/40. Day 16: R does 4/40 (total 39/40). Day 17: K needs to do 1/40. Since K does 2/40 per day, K takes 0.5 days. Total = 16.5 days.