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 option.
A) 6  B) 7  C) 8  D) 4  E) 2

Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 4 no . of days when b works = 4 → 4 x + 4 y = 1 when b starts : no . of days when a works = 5 no . of days when b works = 3 → 5 x + 3 y = 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 : d"
Answer: D