A and B complete a work in 24 and 30 days, respectively, working 10 hours per day. The work is to be done in two shifts. The morning shift is for 6 hours and the evening shift is for 4 hours. On the first day, A works in the morning and B works in the evening, and they interchange their shifts every day. On which day did the work get completed?

Total work LCM = 120 Efficiency of A = total work/total days = 120/24 = 5 Work done by A in 10 hours of one day = 5 Efficiency of B total work / total days = 120/30 Work done by B in 10 hours of one day = 4 On the first day, A works in the morning shift and second day A works in evening shift In two days, A can complete 10 hours of work = 5 On first day B works in evening shift and second day B works in morning shift   In two days, B can complete 10 hours of work = 4 Work done by A and B in two days = 5 + 4 = 9 A and B repeat the same process on 26 days   Work completed by A and B in 26 days = 9 x 13 = 117.   Remaining work = 120-117=3 A and B complete 9 works in 2 days ⇒ 9 = 2 days ⇒ 3 = 2/3 days   A and B complete 3 works in 2/3 days Hence the total time taken to complete the work = 26(2/3) days The total work completed on the 27th day