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?
Choices.
A) 5
B) 4.5
C) 6
D) 7
E) 8
Work done by A &amp; B in a day = x &amp;y respectively.   When A starts:   No. of days when A works = 6No. of days when B works = 4 → 6x + 4y = 1   When B starts:   No. of days when b works = 5 No. of days when A works = 5 → 5x + 5y = 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   5nswer: 5
<result>A</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 10 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?