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.

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. 100 minutes
• B. 150 minutes
• C. 60 minutes
• D. 200 minutes

Answer 1

The Correct Option is D

The problem involves understanding the scheduling of visa applications across different categories. We'll break down the given information to arrive at the solution. There are 4 categories: US, UK, Schengen, and Others, processed at 10 counters. The allocation is: US (4 counters), UK (2 counters), Schengen (2 counters), Others (2 counters). The processing time for the US and UK applications is 10 minutes each. There are twenty 15-minute slots from 9:00 am to 2:00 pm, with each slot scheduled for 10 applications.

Firstly, knowing 50% of the applications are US applications implies that in each slot: 5 US applications, 2 UK, 2 Schengen, and 1 Other application need processing. To confirm:

• Each slot has 10 applications: 5 (US) + 2 (UK) + 2 (Schengen) + 1 (Others) applications

This assignment balances the dedicated counters and application numbers.

We know:

1. All slots were full.
2. Vijay was called at 9:25 am, and the slots fill sequentially but some applicants are processed later (Ira, Vijay, and Nandini arrived late at 9:20 am).

Logical steps:

1. Since 50% of applications are US, 5 out of 10 are US, leaving 5 applications for UK, Schengen, and Others combined.
2. Given the distribution (2 UK, 2 Schengen, 1 Others), each category fits into the schedule without exceeding counter capacity.
3. The Schengen category has a specific scenario with Ira, Vijay, and Nandini arriving late, leading to further delays in processing.
4. With 20 slots running fully, we need to determine maximum processing time exclusively for Others.

Maximum processing time setup, considering Others applications only:

• If 1 per slot, over 20 slots, from 9:00 am to 2:00 pm, then Others category will have 1 per slot processed constantly through 2 counters. Assume processing capability for 1 applicant per 15-minute slot as no other specific processing time is given. Total slots = 20.
• 1 application takes each 15-minute slot fully due to Other applications not written as having a set processing time, equal either to Schengen or UK.

The maximum possible value for processing all "Others" applications (considering the setup): 20 applications * 10 minutes = 200 minutes.

The answer: 200 minutes.