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

In this table, first row gives us the name of 4 categories of visa applications, along with their processing time.

3rd row - consist of counters in each category named as C1, C2,etc.

the blank rows will consist of the time each application will be going from each counter.

We know the total number of applicants = 200

Also, we are given that 50% of the applications were US applications, and the number of US applications was the same in all the slots. The same was true for the other three categories. (Clue 2 &3)

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

For slot 1;

We know, the first slot will start at 9:00 and will end at 9:15 (each slot is of 15 minutes)

Also, we found that in US there are 5 applicants in each slot, but the counters are only 4,

Therefore, the first 4 applicants, will come at 9:00 and will go at 9:10 in each counter (processing time is 10 minutes)

therefore, the 5th applicant, will get number at 9:10 and his application will get completed at 9:20.

With this the first slot of US will be completed.

And, the net slot will start from 9:15.

Now, we know, each slot was of 15 minutes.

Therefore, the first slot will start at 9:00 and will end at 9:15.

At 9:15, as we can see C1 was full, therefore, from the next 5 applicants of 2nd slot, first 3 will come at 9:15 and will go at 9:25 in C2, C3, C4.

and in C1, the 2nd slot applicant will get number at 9:20 (when the 5th applicant of 1st slot will go) and will go at 9:30.

And the last applicant of 2nd slot will get number at 9:25 in C2 and will go at 9:35.

Now, For the 3rd slot,

the 2nd slot will get over at 9:30 (as each slot is of 15 minutes, therefore, 1st slot - 9:00 to 9:15, and 2nd slot, will be from 9:15 to 9:30)

Therefore, applicants of the 3rd slot will come at 9:30 and will find only 2 counters blank (C3 & C4), therefore, the first 2 applicants ,will come at 9:30 and will go at 9:40.

Then the next applicant will get his number at 9:30 and will go at 9:40 in C1, and in the same manner we can form this table.

It is also known that Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order.

and, They had a 9:15 am slot.

Since the number of Schengen applicants was the same in all the slots (clue 2).

=> number of Schengen applicants in each slot is at least 3.

Similarly, it is given that Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category

=> number of other category applicants in each slot is atleast 2.

We know that, the number of total applicants in each slot is 10.

Also, we know total applicant in US = 5, Schengen = atleast 3 and others is atleast 2.

But the sum of all this is already coming to be 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.

Using clue 5,

Vijay was called to a counter at 9:25 am.

Also, Vijay was scheduled for Schengen.

It is given that each US and UK application requires 10 minutes of processing time, and 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.

Therefore, the first applicant in Schengen would have completed his application at 9:12:30 and second at 9:25 , and so on

It is given that,

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.

Also, 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.

Also, we know, Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.

Therefore, For the other applicants, the time taken to process one application is at most 5 minutes.

From the slots, we can see that the first slot took 20 mins to complete, and after that the remaining 19 slots took 15 mins each to complete the US application process.

So, Total time taken = $20 + 15 \times 19 = 305$ mins.

Hence end time will be = 9 AM + 305 Mins = 2:05 P.M.