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 14 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?	Answers.
A) 12	B) 14	C) 10	D) 11	E) 13
Work done by AB in a day = xy respectively.   When A starts:   No. of days when A works = 8No. of days when B works = 6 → 8x + 6y = 1   When B starts:   No. of days when A works = 7No. of days when A works = 7 → 7x + 7y = 1   Solving the above two equations for xy   x = 1/14 y = 1/14   → Total work done by AB in a day = 1/14 + 1/14 = 2/28= 1/14   → No. of days to complete the work when both work together =14   Answer: 14
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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 14 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?