CAT 2019 Slot 2 DILR Question & Solution
Data Set
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?
Solution:
If all the doctors served the patients one after the other, then in 2.5 hrs, Ben will serve 15 patients, Kane will serve 10 patients and Wayne will serve 6 patients.
A total of 31 patients can be served on a particular day.
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?
Solution:
If all the doctors served the patients one after the other, then in 2.5 hrs, Ben will serve 15 patients, Kane will serve 10 patients and Wayne will serve 6 patients.
Ben will earn = 15*100=Rs 1500
Kane will earn = 10*200=Rs 2000
Wayne will earn = 6*300=Rs 1800
So Kane will earn the maximum amount in consultation charges on that day.
Option B
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?
Solution:
Mr Singh is 13th in the sequence on all the three days.
The following table will show the sequence for Monday, Wednesday and Friday.
He will stay the longest when the 13th guy is served by Doctor Wayne.
From the table, on Monday he had to wait at the clinic for the maximum duration: till 10:15.
Option C
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
Solution:
On Thursday, the preference order for the patients is Wayne, Ben and Kane.
The first two customers will be served by Wayne and Ben. While Kane will be empty for the first 15 mins. Then he and Ben will serve the next two customers and Wayne will be empty for 5 minutes as shown in the figure below.
As we can see that the cycle will repeat after every 30 mins.
So all three doctors are never simultaneously free.
Option D