X and Y can complete a piece of work in 8 days and 12 days, respectively. If they work on alternate days, with X working on the first day, how long will it take the duo to complete the work?

Explanation

Given: A and B can separately do a piece of work in 8 and 12 days respectively. Formula used: W = E × T Where, W = Work, E = Efficiency, and T = Time Calculation: Time taken by A = 8 days Time taken by B = 12 days Let Total work = LCM of 8 and 12 = 24 units Efficiency of A = 24/8 = 3 units/day Efficiency of B = 24/12 = 2 units/day Efficiency of A and B together = 3 + 2 = 5 units/2 days By working alternatively, they would complete 20 units of work in 8 days. Remaining work = 24-20 ⇒ 4 units of these 4 units of work, first 3 units would be completed by A(as he started the work) and 1 unit by B. time taken = 1+1/2 ⇒ 1.5 days Total time taken to complete the work = 9.5 days ∴ Total time taken to complete the work is 9.5 days.