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CAT 2023 Slot 1 — DILR Question 5

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.

When did the application processing for all US applicants get over on that day?

Answer & solution

  • A

    3:40 pm

  • 2:05 pm

  • C

    2:25 pm

  • D

    2:00 pm

Solution

Easy

US is the bottleneck: 55 applications arrive every slot but only 44 counters serve them at 1010 min each, so a queue builds. Track the queue to its last finish — and remember to count the idle gap at the very start.

US load. 55 US per slot ×20=100\times 20 = 100 applications, 44 counters, 1010 min each. Slots start at 9:009{:}00 and the last (20th) starts at 1:451{:}45 pm. Each slot adds one more application than the 44 counters clear in that slot, so a backlog accumulates.

1

See the first stall. Slot 9:00 sends 55 US to 44 counters: four run 9:00 ⁣− ⁣9:109{:}00\!-\!9{:}10, the fifth runs 9:10 ⁣− ⁣9:209{:}10\!-\!9{:}20. Meanwhile the counters sit idle 9:10 ⁣− ⁣9:159{:}10\!-\!9{:}15 waiting for the next slot — that lost capacity is exactly what makes the backlog persist.

2

Run the queue to the end. Feeding all 100100 applications through 44 counters first-come-first-served, with each slot releasing 55 at its scheduled time, the last US application clears at:

2:05 pm.\boxed{2{:}05\ \text{pm.}}

(The 55 from the final 1:451{:}45 slot occupy the four counters 1:45 ⁣− ⁣1:551{:}45\!-\!1{:}55, and the leftover fifth runs 1:55 ⁣− ⁣2:051{:}55\!-\!2{:}05.)

Total US work =100×10=1000=100\times 10 = 1000 counter-minutes over 44 counters =250=250 min of pure processing. From 9:009{:}00 that alone reaches 1:101{:}10 pm; the unavoidable start-up idling pushes the finish to the last leftover at 2:05 pm.

All US processing is over at 2:05 pm.

CAT 2023 Slot 1 DILR Q5: When did the application processing for all US applicants get over on that day? — Solution | TheCATExam