CAT 2019 Slot 2 — DILR Question 31
Answer the following questions based on the information given below.
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.
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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.
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?
Answer & solution
- A
Wednesday
Monday
- C
Friday
- D
Same duration on all three days
In first 50 minutes, Dr. Ben sees 5patients; Dr. Kane sees 3 patients and he must be with his four patients while Dr. Wayne sees 2 patients.
These must be first 11 patients. Now about patients with token numbers 12 and 13.
On Monday patient with token number 13 will go to Dr. Wayne, on Wednesday and Friday he will go to Dr. Ben.
Hence, on Monday, he will spend 10 + 50 + 25 = 85 minutes, while on the remaining two days, he will spend 10 + 50 + 10 = 70 minutes.
So, Mr. Singh was at the clinic for the maximum duration on Monday.
Hence, option (b).