Discussion
A and B can complete a piece of work in 12 days and 18 days, respectively. A begins to do the work and they work alternately on their turn. The whole work will be completed in:
Answer: A
The work is completed in 14 1/3 days. A does 1/12 and B does 1/18 of the work a day. Two days (A then B) complete 1/12 + 1/18 = 5/36. Seven such pairs, 14 days, complete 35/36. The remaining 1/36 is done by A on the 15th day in (1/36)/(1/12) = 1/3 day. So the total is 14 1/3 days. 15 1/3 would add a whole extra day and the other two values give wrong remainders. Because they work alternately and A is faster, the pair of days does not end in a whole number of days, and the fractional last day is done by A alone. Option 15 1/3 would add an extra day with B, which is not needed because only 1/36 of the work remains.
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