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 10 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) 5
B) 4.5
C) 6
D) 7
E) 8

Rationale: work done by a & b in a day = x & y respectively . when a starts : no . of days when a works = 6 no . of days when b works = 4 → 6 x + 4 y = 1 when b starts : no . of days when b works = 5 no . of days when a works = 5 → 5 x + 5 y = 1 solving the above two equations for xy x = 1 / 10 y = 1 / 10 → total work done by ab in a day = 1 / 10 + 1 / 10 = 2 / 10 = 1 / 5 → no . of days to complete the work when both work together = 5 answer : a
Answer: A