A, B, and C are working together on a project. A can complete the project alone in 15 days, B in 20 days, and C in 30 days. On the first day, A, B, and C work together. On the second day, A and B work together. On the third day, B and C work together. This pattern repeats in the same order. How many days will it take to complete the entire project?

Total work = (LCM of  15 , 20 and 30) = 60 units Efficiency of A = 60/15 = 4 units/day Efficiency of B = 60/20 = 3 units/day Efficiency of C = 60/30 = 2 units/day ATQ 1st day work (A+B+C) = 4+3+2 = 9units 2ndday work  (A+B) = 4+3 = 7 units 3rd day work (B+C) = 3+2 = 5 units Total work in 3 days = 9+7+5 = 21 units Total work in 6 days = 21 x 2 = 42 units Remaining work = 18units Now its turn of all three on 7thday  (A,B and C) = 9units On 8th day (A and B) = 7 Remaining 2 units of work done by (B and C) = 2/5 days = 0.4 day Total time taken = 8.4 days