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A and B can do a work in 9 days and 12 days respectively. If they work on alternate days starting with A, then in how many days will the work be completed?

Solution

Correct Option: 3

A's 1-day work = 19\frac{1}{9}, B's 1-day work = 112\frac{1}{12}.

In 2 days (A then B): 19+112=736\frac{1}{9} + \frac{1}{12} = \frac{7}{36}.

In 10 days (5 cycles): 3536\frac{35}{36} work done. Remaining: 136\frac{1}{36}.

On day 11, A works: time = 1/361/9=14\frac{1/36}{1/9} = \frac{1}{4} day.

Total = 101410\frac{1}{4} days.

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