Question:
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]
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]
Updated On: Aug 17, 2024
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The Correct Option is A
Solution and Explanation
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.
So, the total number of applicants is 200 (20 slots * 10 applications per slot).
50% of the applications are from the US, and the number of US applications is the same in each slot. The same applies to the other three categories.
So, the total number of US applicants is 100 (200 * 50%), and the number of US applicants in each slot is 5 (100 / 20).
Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at the 9:15 am slot. Since the number of Schengen applicants is the same in each slot, there must be at least 3 Schengen applicants per slot.
Mahira and Osman were scheduled in the 9:30 am slot for visa processing in the Others category, so there are at least 2 applicants in the Others category per slot.
Since there are 10 applicants per slot, and we already have 3 Schengen and 2 Others applicants, there are no UK applicants in each slot.
There are 10 counters in total, with 4 dedicated to US applications and 2 each for UK, Schengen, and Others. Each US and UK application takes 10 minutes to process. Vijay, who was 5th in the queue, was called to a counter at 9:25 am. This implies that the processing time for Schengen applications is 12.5 minutes.
| US (10 min) | schengen(12.5 min) | Others (5 min process) | |||||
| 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 particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at 9:15 am but entered the VPO at 9:20 am. When they entered, 6 out of the 10 counters were processing applications or had just finished and were ready to start new ones. Thus, there were 4 free counters: 2 UK and 2 Others (since the US and Schengen counters were busy or had just finished processing).
From the table, the number of UK applicants in each slot is zero, so the total number of UK applicants is zero.
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