CAT 2019 Slot 2 — DILR Question 32
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.
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
Answer & solution
0
- B
30
- C
10
- D
15
Patient with token no. 1 will be seen by Dr. Wayne for 25 minutes and that with token number 2 will be seen by Dr. Ben for 10 minutes.
Now the two patients those entered at 9:15 a.m were given tokens with numbers 3 and 4.
These will be seen by Dr. Ben and Dr. Kane respectively.
As Dr. Kane takes 15 minutes to examine one patient, he will be free at 9:30 am.
Thus, in first half an hour three doctors will not be simultaneously free.
This is true for duration of 30 minutes henceforth.
Thus the total duration in minutes when all three doctors are simultaneously free will be 0.
Hence, option (a).