# Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne - CAT DILR questions – Logical Reasoning

## CAT 2019 - Slot 2 - Question 2 - Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne

### 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.

Q. 1: What is the maximum number of patients that the clinic can cater to on any single day?

1. 12

2. 30

3. 15

4. 31

1. As clinic is open for 150 mins max patients for each doctor wi be as follows

Ben = 150/10 = 15

Kane = 150/15 = 10

Wayne = 150/25 = 6

Total = 15 + 10 + 6 = 31

Q. 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?

1. Dr. Ben

2. Dr. Kane

3. Both Dr. Wayne and Dr. Kane

4. Dr. Wayne

2. On a day with max patients

Ben would have = 15×100 = 1500

Kane would have = 10×200 = 2000

Wayne would have 6×300 = 1800

Maximum amount can be earned by Dr. Kane

Q. 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?

1. Friday

2. Same duration on all three days

3. Wednesday

4. Monday

3. On each day , it can be seen that in first 60 minutes a total of 12 patient can be seen by the doctors and 13th will be in a room in which Dr. Wayne will be seeing him.

To stay for the maximum time in the clinic the 13th no patient must go in the room of Dr. Wayne.

As 12th and 13th no of patient will visited by one of the doctors Dr Ben or Dr Wayne . So for 13th no of patent to visit Dr Wayne , Dr Wayne must be in the room which is numbered higher than Dr Ben’s room number. It is happing only on Monday when Dr Ben is in room 1 and Dr Wayne is in room 3.

Q. 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

1. 30

2. 10

3. 0

4. 15

4. At 9 AM 2 patient are waiting till 9:15 again 2 patients would be waiting. At 9:30 none of the patients would be waiting. Hence all 3 will never be free at same time. Hence 0.

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