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 exactly 12 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?	Choose the correct choice from the following answers:
A) 4  B) 4.5  C) 6  D) 8  E) 6.5
Work done by AB in a day = xy respectively.   When A starts:   No. of days when A works = 6No. of days when B works = 6 → 6x + 6y = 1   When B starts:   No. of days when A works = 6.5No. of days when B works =5.5 → 6.5x +5.5y = 1   Solving the above two equations for xy   x = 1/12 y = 1/12   → Total work done by AB in a day = 1/12 + 1/12 = 2/12 =1/6   → No. of days to complete the work when both work together = 6   Answer: 6
<result>C</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 exactly 12 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?