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. 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.
Question: 1
What is the maximum number of patients that the clinic can cater to on any single day?
Between 9:30 AM and 11:30 AM, which is a total of 150 minutes, Doctors Ben, Kane, and Wayne take 10, 15, and 20 minutes, respectively, for each patient. Consequently, Ben, Kane, and Wayne can attend to 15, 10, and 6 patients, respectively, within this time frame. Therefore, the maximum number of patients they can collectively see every day is 31.
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Question: 2
The queue is never empty on one particular Saturday. Which of the three doctors would earn the maximum amount in consultation charges on that day?
Given that on Saturday the queue is not empty implies that each doctor sees the maximum number of patients on a day.
Additionally, Ben, Kane, and Wayne charge Rs. 100, 200, and 300, respectively.
Therefore, the earnings for each doctor are as follows:
Ben earns 15 (100) = Rs. 1500,
Kane earns 10 (200) = Rs. 2000,
Wayne earns 6 (300) = Rs. 1800.
Hence, Kane earns the maximum amount.
Answer: (Dr. Kane)
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Question: 3
Mr. Singh visited the clinic on Monday, Wednesday, and Friday of a particular week, arriving at 8:50 a.m. on each of the three days. His token number was 13 on all three days. On which day was he at the clinic for the maximum duration?
Mr. Singh takes the maximum duration when he enters Dr. Wayne's room, who sees each patient for 25 minutes. On Monday, he was at the clinic for 85 minutes. Similarly, on Wednesday, he would meet Ben, and he would be at the clinic for 70 minutes. On Friday, he would meet Ben again, and he would be at the clinic for 70 minutes.
Therefore, Singh stays at the clinic for the maximum duration on Monday.
Answer: (Monday)
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Question: 4
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
