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

Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 6 → 6 x + 6 y = 1 when b starts : no . of days when a works = 6.5 no . of days when b works = 5.5 → 6.5 x + 5.5 y = 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 : c"
Answer: C