A can complete a task in 20 days, and B can complete it in 25 days. When B and C collaborate, they can finish the same task in 75/8 days. Now, if A and C initiate the work together and after 6 days, B takes over from C, how many days will it take to complete the entire task?

ATQ, Let total amount of work = LCM of 20, 25, 75/8 = (LCM of 20, 25,75)/(HCF of 1, 1, 8) = 300 units Amount of work done by A in one day = 300/20 = 15 units Amount of work done by B in one day = 300/ 25 = 12 units Amount of work done by B and C in one day = 300/ (75/8) = 32 Amount of work done by C in one day = 32 – 12 = 20 units Amount of work done by A and C in 6 day = (15 + 20) × 6 = 210 Rest work = 300 – 210 = 90 units Rest work done by A and B = 90/(12 + 15) = 90/27 = 10/3 days Total time taken to complete the work = 6 + 10/3 = 28/3 days