Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for 10 minutes and charges Rs. 100/-. Dr. Kane sees each patient for 15 minutes and charges Rs. 200/-, while Dr. Wayne sees each patient for 25 minutes and charges Rs. 300/-.
The clinic has three rooms numbered 1, 2 and 3 which are assigned to the three doctors as per the following table.
| Room No. | Monday & Tuesday | Wednesday & Thursday | Friday & Saturday |
|---|---|---|---|
| Ben | Wayne | Kane | |
| Kane | Ben | Wayne | |
| Wayne | Kane | Ben |
The clinic is open from 9 a.m. to 11.30 a.m. every Monday to Saturday.
On arrival each patient is handed a numbered token indicating their position in the queue, starting with token number 1 every day. As soon as any doctor becomes free, the next patient in the queue enters that emptied room for consultation. If at any time, more than one room is free then the waiting patient enters the room with the smallest number. For example, if the next two patients in the queue have token numbers 7 and 8 and if rooms numbered 1 and 3 are free, then patient with token number 7 enters room number 1 and patient with token number 8 enters room number 3.
On a slow Thursday, only two patients are waiting at 9 a.m. After that two patients keep arriving at exact 15 minute intervals starting at 9:15 a.m. -- i.e. at 9:15 a.m., 9:30 a.m., 9:45 a.m. etc. Then the total duration in minutes when all three doctors are simultaneously free is
Correct Answer :
0
Solution :
We track the schedule of the three doctors starting from 9:00 a.m. on Thursday.
1. At 9:00 a.m., there are 2 patients. They are assigned to the available doctors according to their priority rules, leaving the third doctor free.
2. At 15-minute intervals (9:15, 9:30, 9:45, etc.), new patients arrive and are allocated to doctors who have finished their previous appointments.
By drawing a timeline of when each doctor is busy with a patient and when they finish, we can sum the non-overlapping intervals during the day where all three doctors are unoccupied at the same time.
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