Instructions

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 forÂ UK applications, Schengen applications and Others applications. Applicants are called inÂ for processing sequentially on a first-come-first-served basis whenever a counter getsÂ freed for their category. The processing time for an application is the same within eachÂ category. But it may vary across the categories. Each US and UK application requires 10Â minutes of processing time. Depending on the number of applications in a category andÂ time required to process an application for that category, it is possible that an applicant forÂ a slot may be processed later.

On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing inÂ that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they enteredÂ the office, exactly six out of the ten counters were either processing applications, or hadÂ 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 inÂ the Others category.

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.

Question 1

# How many UK applications were scheduled on that day?

Solution

It is given thatÂ 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.

Hence, the total number of applicants = (20*10) = 200. It is also known thatÂ 50% of the applications were US applications, andÂ the number of US applications was the same in all the slots. The same was true for the other three categories.

Hence, the number of total number of US applicants = (200*50%) = 100, and the number of US applicants in each slot = (100/20) = 5

It is also known thatÂ Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot. Since the number of Schengen applicants was the same in all the slots, it implies the number of Schengen applicants in each slot is at least 3.Â

Similarly, it is given thatÂ Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category, which implies the number of other category applicants in each slot is at least 2. Since the number of total applicants in each slot is 10, this implies the number of Schengen and other applicants in each slot is 3, and 2, respectively. Hence, the number of UK applicants is 0 in each slot.

It is also known that the number of total counters is 10,Â among whichÂ four are dedicated to US applications, and two each for UK applications, Schengen applications, and Others applications. It is given thatÂ each US and UK application requires 10 minutes of processing time, andÂ Vijay was called to a counter at 9:25 am. (Who is 5th in the queue). It can only be possible when the processing time of Schengen applications is 12.5 minutes.

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. Hence, at 9.20 am, there are exactly four free counters. Out of these 4, 2 is the UK counter, and the other two are other counters. (Since the US counters and Schengen CountersÂ were either processing applications, or had finished processing one and were ready to start processing the next.)

From the table, we can say that the total number of UK applicants in each slot is zero, Hence, the total number of applicants is zero.