At a certain factory, 4 processesA, B, C, and Dare carried out 24 ho

At a certain factory, 4 processes—A, B, C, and D—are carried out 24 hours per day, 7 days per week. Process A operates on a 60-hour cycle; that is, Process A takes 60 hours to complete and immediately begins again when it is completed. Likewise, Process B operates on a 24-hour cycle, Process C operates on a 27-hour cycle, and Process D operates on a 9-hour cycle. On Monday, all 4 processes began together at 10:00 in the morning.

A day is 24 hours. So, a process will restart at 10 am any time the process has operated full cycles for a multiple of 24 hours.

Thus, we know the following for each process:

For A, the first multiple of 24 such that it will have operated for full cycles for a multiple of 24 hours is 2 x 60 = 120 hours. 120/24 = 5 days.

B operates a full cycle every 24 hours. So, B always starts at 10 am.

C operates for for 27 = 3 × 3 × 3 hours each cycle. 24 = 3 × 8. So, to get to a multiple of 24, C must go through 8 complete cycles or 8 × 27 = 216 hours = 9 days.

D operates for 9 hours each cycle. 24 = 3 × 8. So, to get to a multiple of 24, D must go through 8 complete cycles or 8 × 9 = 72 hours = 3 days.

On the basis of the information provided, select for Processes A, B, and D the day of the week on which Processes A, B, and D will next begin together at 10:00 in the morning.

We can ignore B since B begins at 10 in the morning every day.

A begins at 10 in the morning every 5 days, and D does every 3 days.

The least common multiple of 5 and 3 is 15. So, the three processes will next begin together after 15 days.

15 days is 2 weeks and 1 day later.

Two weeks and 1 day later than Monday is Tuesday.

For Processes A, B, and D, select Tuesday.

Also select for All 4 processes the day of the week on which Processes A–D will next begin together at 10:00 in the morning. Make only two selections, one in each column.

For this one, B still doesn't matter since it starts at 10 in the morning every day.

Also, we can ignore D since the cycle time of 27 hours for C is a multiple of the cycle time of 9 hours for D. So, D will always start at 10 in the morning when C does.

Thus, this question can be answered through determining when A and C will both start at 10 in the morning again.

A begins at 10 in the morning every 5 days. C does every 9 days.

The least common multiple of 5 and 9 is 45. So, they will begin together again 45 days later.

So, A and C will next begin again synch 6 weeks and 3 days later.

3 days after Monday is Thursday.

For All four processes select Thursday.

Correct answer:

Very interesting question, looks complicated but follows a simple process:
First Q: Answer is Tuesday.
Logic: LCM of A, B and D is 360, that translates to the fact that these three will again process together after 360hrs which is effectively 15 days from the current Monday. Therefore the 15th day after the Monday is a Tuesday.
Second Q: Answer is Thursday
Logic is same as that of Q1, LCM of the 4 processes is 1080hrs which is 45 days that translates to a Thursday.

Posted from my mobile device

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I made a counting mistake. Starting Monday, the next Monday is 8th day, so i chose Monday as 15th day.
Later i realised Monday 10:00 to Tuesday 10:00 counts as 1 day.
Thank you very much Sir! ­