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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 B

Bunuel
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


Are You Up For the Challenge: 700 Level Questions
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Bunuel
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


Are You Up For the Challenge: 700 Level Questions
Let the total work be 24 units

So, Individual efficiencies of the individuals are 3 & 2

Since, they work alternatively, they complete 5 units in 2 days

Thus, they complete 20 units in 8 days and are left with 4 units withich will be completed as

Jack - 3 units in 1 day and 1 more unit left for Jill to complete in 1/2 days..
.
Hence, total time taken to complete the task is 9 & 1/2 days, Answer must be (A)
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Bunuel
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


Are You Up For the Challenge: 700 Level Questions

Their combined rate is 1/8 + 1/12 = 3/24 + 2/24 = 5/24. Since they work on alternate days, 5/24 of the job is actually done in 2 days, and thus 5/24 x 4 = 20/24 = 10/12 of the job will be done in 8 days. On the 9th day, Jill will complete another 1/12 of the job, so a total of 10/12 + 1/12 = 11/12 of the job will be completed. The last 1/12 of the job will be completed by Jack in (1/12)/(1/8) = 8/12 = 2/3 of a day. Therefore, the entire job will be completed in 9 ⅔ days.

Answer: B
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