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by anuprajan5 » Tue Oct 02, 2012 9:51 pm
Let's take the least common multiple for these 2work rates - The LCM is 36.

Assume they have to create 36 items each.

A can complete 4 in a day (36/9)
B can complete 3 in a day (36/12)


Since the sequence starts with A, they can complete 35 items in 10 days (4+3+4+3+4+3+4+3+4+3). Since it's A's turn next, he can complete 1 item in 1/4 day

therefore total- 10+1/4 = 41/4

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by GMATGuruNY » Wed Oct 03, 2012 3:43 am
rrobiinn wrote:A & B working alone can do a work in 9 and 12 days respectavily. If they work for a day alternately, A beginning, in how many days the work will be completed?

Ans: 41/4 days.
Let the job = 36 units.

Rate for A = w/t = 36/9 = 4 units per day.
Rate for B = w/t = 36/12 = 3 units per day.

When A and B alternate, the amount of work produced every 2 days = 4+3 = 7 units.
Thus, the number of 2-DAY PERIODS required to produce 35 units = 35/7 = 5, implying 2*5 = 10 days.

Time for A to produce the remaining 1 unit on the last day = w/r = 1/4.

Total time = 10 1/4 days.
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by sureshbala » Wed Oct 03, 2012 3:48 am
Amount of work done in 2 days = 1/9 + 1/12 = 7/36
In 10 days 35/36 Work is done
The remaining 1/36 will be handled by A and he can finish this off in 1/4 of a day
Hence, 10 + 1/4 = 41/4
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