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. Applications 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 were 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:

Question 1

How many UK applications were scheduled on that day?

Question 2

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?

Question 3

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

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

Question 4

Which of the following statements is false?

A. The application process of Osman was completed before 9:45 am.
B. The application process of Mahira started after Nandini’s.
C. The application process of Osman was completed before Vijay’s.
D. The application process of Mahira was completed before Nandini’s.

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Set 1(Check the below table for the detailed slot details)

Question 1

Total slots = 20
Applications per slot = 10
Total applications = 20 × 10 = 200
50% are US applications, so US applications = 100
US applications per slot = 100 ÷ 20 = 5

Since every slot has 10 applications:
US + UK + Schengen + Others = 10
5 + UK + Schengen + Others = 10
So, UK + Schengen + Others = 5

Ira, Vijay and Nandini were scheduled for Schengen in the 9:15 slot, so Schengen per slot must be at least 3.
Mahira and Osman were scheduled for Others in the 9:30 slot, so Others per slot must be at least 2.
Therefore:
Schengen = 3
Others = 2
UK = 0

So, UK applications scheduled that day = 0

Question 1 → 0

There were 0 UK applications scheduled on that day.

Question 2

Finding maximum processing time for Others

Others applications per slot = 2
Others counters = 2

At 9:00, 2 Others applicants arrive and both counters start processing.
At 9:15, the next 2 Others applicants arrive.

At 9:20, exactly 6 counters were active/ready.
US counters at 9:20 = 4 active
Schengen counters at 9:20 = 2 active/ready
That already gives 6 counters.

So, Others counters must be free at 9:20.
This means the 9:15 Others applicants must have finished by 9:20.

Therefore, Others processing time can be at most 5 minutes.

Total Others applications = 2 per slot × 20 slots = 40
Maximum total processing time = 40 × 5 = 200 minutes

Question 2: 200

Question 3

Finding Schengen processing time

Schengen has 2 counters.
There are 3 Schengen applications per slot.

At 9:00, 3 Schengen applicants arrive.
2 start immediately at 9:00.
1 waits.

Let Schengen processing time = S minutes.

For Vijay to be called at 9:25, the following works:

At 9:00, first two Schengen applicants start.
They finish at 9:12:30 if S = 12.5 minutes.
Then the third 9:00 applicant starts at 9:12:30 and finishes at 9:25.

Ira, Vijay and Nandini arrive late at 9:20.
At 9:20, one Schengen counter is free, so Ira starts at 9:20.
At 9:25, the other Schengen counter becomes free, so Vijay starts at 9:25.
This matches the condition given.

So, Schengen processing time = 12.5 minutes

Nandini starts when Ira finishes:
Ira starts at 9:20
Ira finishes at 9:32:30
So Nandini starts at 9:32:30

Nandini finishes after 12.5 minutes:
9:32:30 + 12.5 minutes = 9:45 am

Question 3:

D) 9:45 AM

Question 4

For Mahira and Osman

Mahira and Osman are Others applicants in the 9:30 slot.
Others processing time is at most 5 minutes.
So both start at 9:30 and finish by 9:35.

Vijay starts at 9:25 and finishes at 9:37:30.
Nandini starts at 9:32:30 and finishes at 9:45.

Now check the statements:

A. Osman completed before 9:45 am → True
B. Mahira started after Nandini → False, because Mahira started at 9:30, Nandini started at 9:32:30
C. Osman completed before Vijay → True
D. Mahira completed before Nandini → True

Question 4

The false statement is:

B. The application process of Mahira started after Nandini’s.