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:
- All slots were full.
- The number of US applications was the same in all the slots. The same was true for the other three categories.
- 50% of the applications were US applications.
- All applicants except Ira, Vijay and Nandini arrived on time.
- Vijay was called to a counter at 9:25 am.
What is the maximum possible value of the total time (in minutes, nearest to its integer value) required to process all applications in the Others category 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:
- All slots were full.
- The number of US applications was the same in all the slots. The same was true for the other three categories.
- 50% of the applications were US applications.
- All applicants except Ira, Vijay and Nandini arrived on time.
- Vijay was called to a counter at 9:25 am.
What is the maximum possible value of the total time (in minutes, nearest to its integer value) required to process all applications in the Others category on that day? [This question was asked as TITA]
- 100 minutes
- 150 minutes
- 60 minutes
- 200 minutes
The Correct Option is D
Solution and Explanation
- Each slot accommodates 10 applications: 5 (US) + 2 (UK) + 2 (Schengen) + 1 (Others)
- All available slots were fully utilized.
- Vijay was called at 9:25 am. Slots are filled sequentially, but some applicants (Ira, Vijay, and Nandini) arrived late at 9:20 am, potentially causing processing delays.
- With 50% US applications, 5 out of 10 applications per slot are US, leaving 5 for UK, Schengen, and Others combined.
- The distribution of 2 UK, 2 Schengen, and 1 Other per slot fits within counter capacities.
- The Schengen category presents a special case due to late arrivals of Ira, Vijay, and Nandini, which could further delay processing.
- With 20 fully occupied slots, the objective is to determine the maximum processing time for "Others" applications exclusively.
- Assuming one "Other" application per slot processed continuously across 2 counters from 9:00 am to 2:00 pm (20 slots). Processing time for "Others" is not specified, so it's assumed to be 15 minutes per application, equivalent to a full slot. Total slots = 20.
- Each "Other" application occupies a full 15-minute slot.
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