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. 29 What is the maximum number of patients that the clinic can cater to on any single day?
1) 15 2) 31 3) 30 4) 12
Q. 30 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. Wayne 2) Both Dr. Wayne and Dr. Kane 3) Dr. Ben 4) Dr. Kane
Q. 31 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) Same duration on all three days 2) Monday 3) Friday 4) Wednesday
Q. 32 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) 15 2) 0 3) 10 4) 30
✅ Given Data (Clinic Timing and Doctor Details)
- Clinic Hours: 8:30 AM to 11:00 AM → 2.5 hours = 150 minutes
- 3 Doctors:
| Doctor | Time per Patient | Fee per Patient |
|---|---|---|
| Dr. Ben | 10 minutes | ₹100 |
| Dr. Kane | 15 minutes | ₹200 |
| Dr. Wayne | 25 minutes | ₹300 |
🟦 Q.29 What is the maximum number of patients that the clinic can cater to on any single day?
Step-by-Step:
Each doctor operates independently in 150 minutes:
- Dr. Ben: 150 ÷ 10 = 15 patients
- Dr. Kane: 150 ÷ 15 = 10 patients
- Dr. Wayne: 150 ÷ 25 = 6 patients
✅ Total patients = 15 + 10 + 6 = 31
Correct Answer: Option 2) 31
🟦 Q.30 The queue is never empty on a Saturday. Who earns the most?
Assume all doctors are continuously busy for full 150 minutes.
From Q.29 we already know how many patients each serves:
- Dr. Ben: 15 × ₹100 = ₹1500
- Dr. Kane: 10 × ₹200 = ₹2000
- Dr. Wayne: 6 × ₹300 = ₹1800
✅ Highest Earning: Dr. Kane
Correct Answer: Option 4) Dr. Kane
🟦 Q.31 Mr. Singh visits Mon, Wed, Fri at 8:50 AM and always has Token #13. On which day is he at the clinic the longest?
We need to see when he gets served on each day, assuming each doctor has their own queue.
➤ Monday – Dr. Ben
- Ben sees one patient every 10 mins → Token #13 starts at:
8:30+(12×10)=10:308:30 + (12 × 10) = 10:30, ends at 10:40 - Singh arrived at 8:50 → stays till 10:40 → Total = 110 mins
➤ Wednesday – Dr. Wayne
- Wayne sees one every 25 mins → Token #13 starts at:
8:30+(12×25)=8:30+300=1:30PM8:30 + (12 × 25) = 8:30 + 300 = 1:30 PM
⛔ But clinic ends at 11:00 AM (150 mins max)
→ Max patients = ⌊150/25⌋ = 6
→ Token #13 not served
➤ Friday – Dr. Kane
- Kane sees one every 15 mins → Token #13 starts at:
8:30+(12×15)=11:30AM8:30 + (12 × 15) = 11:30 AM ⛔ Clinic ends at 11:00 AM
→ Max patients = ⌊150/15⌋ = 10
→ Token #13 not served
✅ Only Monday: Token #13 is served. Time = 110 mins
Correct Answer: Option 2) Monday
🟦 Q.32 On a slow Thursday, only 2 patients are present at 9:00 AM. After that, 2 patients arrive every 15 mins starting at 9:15. What is the duration (in mins) when all 3 doctors are simultaneously free?
✅ Q.32 Recap:
On a slow Thursday, only two patients are waiting at 9 a.m. After that, two patients arrive at exact 15-minute intervals starting from 9:15 a.m. (i.e., at 9:15, 9:30, 9:45, …).
What is the total duration (in minutes) when all three doctors are simultaneously free?
✅ What the diagram shows:
- Doctor Preference Order on Thursday:
Patients are assigned in this order: Wayne → Ben → Kane
🔄 Let’s walk through the timeline shown:
At 9:00 AM:
- 2 patients are waiting:
- Patient 1 → Wayne (25 mins) → 9:00 to 9:25
- Patient 2 → Ben (10 mins) → 9:00 to 9:10
- Kane is idle from 9:00 to 9:15 (no patient)
✅ All 3 doctors are not idle together.
From 9:10 to 9:15:
- Wayne is still busy (Patient 1)
- Ben is free (finished at 9:10)
- Kane still idle
Only Ben & Kane are idle here — not all 3
At 9:15:
- 2 new patients arrive:
- Patient 3 → Ben (9:15 to 9:25)
- Patient 4 → Kane (9:15 to 9:30)
- Wayne becomes free at 9:25
So:
- From 9:25 to 9:30:
- Wayne is free
- Ben still with Patient 3 till 9:25
- Kane busy till 9:30
Again, no time when all 3 are free
🌀 Key Insight:
- Every 30-minute cycle, same pattern repeats
- At no point in any cycle do all 3 doctors have idle time overlapping
✅ Final Explanation:
As shown in the diagram, at least one doctor is always with a patient due to the staggered timing and patient assignment rule.
Hence, there is no interval when all 3 doctors are simultaneously free.
✅ Correct Answer:
Option 2) 0 minutes
✅ Final Answer Summary:
| Q. No | Answer | Explanation |
|---|---|---|
| Q29 | 2) 31 | Max patients by Ben (15), Kane (10), Wayne (6) |
| Q30 | 4) Dr. Kane | ₹2000 > ₹1800 > ₹1500 |
| Q31 | 2) Monday | Only Ben could serve Token 13 within clinic hours |
| Q32 | 4) 0 | All 3 doctors never free |
