Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exact 8 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?  Choose the correct choice from the following:
A) 6	B) 7	C) 8	D) 4	E) 2
Work done by AB in a day = xy respectively.   When A starts:   No. of days when A works = 4No. of days when B works = 4 → 4x + 4y = 1   When B starts:   No. of days when A works = 5No. of days when B works = 3 → 5x + 3y = 1   Solving the above two equations for xy   x = 1/8 y = 1/8   → Total work done by AB in a day = 1/8 + 1/8 = 1/4   → No. of days to complete the work when both work together = 4   Answer: 4
<result>D</result>
Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exact 8 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?