CAT 2023 Slot 1 — DILR Question 3

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.

Which of the following is the closest to the time when Nandini’s application process got over?

Answer & solution

A
9:35 am
B
9:37 am
9:45 am
D
9:50 am

Solution

Easy

Track the two Schengen counters from 9:00. The early backlog tells us the Schengen processing time; then walk the late-arriving trio (Ira, Vijay, Nandini) through the two counters in order.

Schengen facts. $3$ Schengen per slot, $2$ counters. The 9:00 slot has $3$ Schengen ( $a_1,a_2,a_3$ ). The trio had the 9:15 slot but entered only at 9:20, in the order Ira → Vijay → Nandini. Given: Vijay was called at 9:25.

Find the Schengen time $T$ from Vijay's start. The 9:00 trio fill both counters: $a_1,a_2$ run $9{:}00\to 9{:}00{+}T$ ; $a_3$ takes the first freed counter, finishing at $2T$ minutes past 9:00. When the trio enter at 9:20 one counter is free (Ira sits at 9:20) and the other is still running $a_3$ . Vijay is called the instant $a_3$ ends:

2T = 25\ \text{min} \;\Rightarrow\; T = 12.5\ \text{min.}

Place the trio. Two counters, served first-come-first-served:

\begin{aligned} &\text{Ira: } 9{:}20 \to 9{:}32{:}30\\ &\text{Vijay: } 9{:}25 \to 9{:}37{:}30\\ &\text{Nandini: starts when Ira's counter frees at } 9{:}32{:}30 \end{aligned}

Finish Nandini. She runs one $12.5$ -minute slot from $9{:}32{:}30$ :

9{:}32{:}30 + 12.5\ \text{min} = 9{:}45.

Nandini's processing is over at 9:45 am.