I find the best way to do such questions is to take the rates of each member.
Assume total work = LCM(8,12) = 24 units.
Now Jack completes 3 units of work in a day and Jill completes 2 units of work in a day.
The question asks how many days will it take if they work alternately with Jill starting the work.
On 1st day, 2 units of work is completed and on second day 3 units of work is completed.
So, a total of 5 units is completed in 2 days. and 20 units will be completed in 8 days.
On the 9th day, Jill will complete 2 units.
Now, a total of 22 units has been completed and 2 units out of 24 units is remaining.
Jack has to do only 2 units of work out of the 3 units that he completes daily.
Time taken by Jack = \(\frac{2}{3}\) days.
Total time taken to complete the work is \(9 \frac{2}{3}\) days.
IMO BBunuel
Jack and Jill working separately complete a work in 8 days and 12 days respectively. If they work on alternate days starting with Jill on the first day, in how many days will the work be completed?
(A) \(9 \frac{1}{2}\) days
(B) \(9 \frac{2}{3}\) days
(C) \(10\) days
(D) \(10 \frac{8}{12}\) days
(E) \(12\) days
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