Solution
Understanding the set :-
This set is a logical reasoning and scheduling problem
- Here we are given information about a clinic -
a) Open: Monday to Saturday
b) Time: 9:00 AM – 11:30 AM → 150 minutes total per day
- Also, we are given details of each doctor as -
| Doctor | Time per Patient | Charge per Patient |
|---|---|---|
| Ben | 10 minutes | ₹100 |
| Kane | 15 minutes | ₹200 |
| Wayne | 25 minutes | ₹300 |
=> So, in 150 minutes:
a) Ben can see 15 patients
b) Kane can see 10 patients
c) Wayne can see 6 patients
- There is a room schedule as -
| Room No. | Mon & Tue | Wed & Thu | Fri & Sat |
|---|---|---|---|
| 1 | Ben | Wayne | Kane |
| 2 | Kane | Ben | Wayne |
| 3 | Wayne | Kane | Ben |
So, the doctors rotate across rooms based on days.
- Also, there is a token system -
i) Patients enter the clinic and receive tokens (1, 2, 3, ...).
ii) When any doctor becomes free, the next patient in the queue goes in.
iii) If multiple rooms are free, patient with lowest token chooses the smallest numbered room.
Example:
If token 7 is next and rooms 1 and 3 are free, token 7 → Room 1
and, Token 8 → Room 3
Now, lets try to solve the set using these clues.
Maximum number of patients can be catered on single day when The queue is never empty and all doctors work to full capacity.
The clinic is open from 9 a.m. to 11.30 a.m i.e. for 150 minutes every day.
Maximum number of patients that can be seen by Dr. Ben are
Maximum number of patients that can be seen by Dr. Kane are
Maximum number of patients that can be seen by Dr. Dr. Wayne are
So the maximum number of patients that the clinic can cater to on any single day are=