CAT 2023 Slot 1 — DILR Question 2

Mixed PracticeEasy

Passage / Data

Answer the following questions based on the information given below:

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?

Answer & solution

Answer: 200

Solution

Easy

"Total time to process all Others" means the sum of processing time over every Others application. It is largest when the per-application Others time is as large as the data allows, so first bound that time, then multiply by the count.

What we know. Others $=2$ per slot $\times 20 = 40$ applications, served at $2$ dedicated counters. The Others processing time is not stated outright; it is capped by the "exactly six counters busy at 9:20" snapshot.

Count Others per day. $2$ Others scheduled in each of the $20$ slots:

2\times 20 = 40\ \text{Others applications.}

Bound the Others time from the 9:20 snapshot. At 9:20 all $4$ US counters are engaged and one Schengen counter is still finishing the early backlog. For the total to stay at exactly six, the two Others counters must not add fresh load — i.e. the $9{:}15$ Others must already be finishing by $9{:}20$ . That forces the per-application Others time to be at most

T_{\text{Others}}\le 5\ \text{min.}

Maximise. Take the largest allowed time, $5$ minutes, for each of the $40$ applications:

40\times 5 = 200\ \text{minutes.}

\mathbf{200}\ \text{minutes}