A visa processing office (VPO) accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
How many UK applications were scheduled on that day? [This question was asked as TITA]
A visa processing office (VPO) accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
How many UK applications were scheduled on that day? [This question was asked as TITA]
- 0
- 1
- 2
- 3
The Correct Option is A
Solution and Explanation
Applications are processed in 20 fifteen-minute slots, from 9:00 am to 2:00 pm, with 10 applications per slot.
The total applicant count is \( 200 \) (20 slots × 10 applications/slot).
US applications constitute 50% of the total, distributed equally across all slots. The same distribution applies to the other three categories.
Therefore, there are \( 100 \) US applicants in total (\( 200 \times 50\% \)), with \( \frac{100}{20} = 5 \) US applicants per slot.
Ira, Vijay, and Nandini were scheduled for Schengen processing consecutively at the 9:15 am slot. As Schengen applicant numbers are uniform per slot, each slot must have at least 3 Schengen applicants.
Mahira and Osman were scheduled for 'Others' category processing at the 9:30 am slot, indicating a minimum of 2 'Others' applicants per slot.
Given 10 applicants per slot (3 Schengen + 2 Others), there are no UK applicants in any slot.
There are 10 processing counters: 4 for US, 2 for UK, 2 for Schengen, and 2 for Others. US and UK applications require 10 minutes processing time. Vijay, fifth in line, was called at 9:25 am, suggesting a Schengen application processing time of 12.5 minutes.
| US (10 min) | Schengen (12.5 min) | Others (5 min) | |||||
|---|---|---|---|---|---|---|---|
| End Time | End Time | End Time | |||||
| C1 | C2 | C3 | C4 | C1 | C2 | C1 | C2 |
| 9:10 | 9:10 | 9:10 | 9:10 | 9:12:30 | 9:12:30 | 9:05 | 9:05 |
| 9:20 | 9:25 | 9:25 | 9:25 | 9:25 | 9:32:30 | 9:20 | 9:20 |
| 9:30 | 9:35 | 9:40 | 9:40 | 9:37:30 | 9:45 | 9:35 | 9:35 |
| 9:40 | 9:45 | 9:50 | 9:55 | ||||
| 9:55 | 9:55 | 10:00 | 10:05 | ||||
| 10:10 | 10:10 | 10:10 | 10:15 | ||||
| 10:20 | |||||||
On a specific day, Ira, Vijay, and Nandini, scheduled for Schengen processing at 9:15 am, arrived at the VPO at 9:20 am. At their arrival, 6 out of 10 counters were actively processing or had just completed applications. This left 4 counters free: 2 for UK and 2 for Others, as US and Schengen counters were occupied or had just finished.
The table indicates zero UK applicants per slot, thus the total number of UK applicants is \( \boxed{0} \).
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