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.

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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

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.

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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?

Accepted Answer

#### **Key Information:**
1. **Total Applications Scheduled:**  
   - There are 20 slots, each with 10 applications.  
   - Total applications = $$ 20 	imes 10 = 200 $$.

2. **Distribution of Applications Across Categories:**  
   - 50% of the applications were US applications.  
     $$ 	ext{US applications} = 200 	imes 0.5 = 100 $$.  
     $$ 	ext{US applications per slot} = \frac{100}{20} = 5 $$.  
   - Remaining applications (UK, Schengen, Others) = $$ 200 - 100 = 100 $$.

3. **Minimum Applications per Slot for Others:**  
   - Each slot has at least **2 Others applications**, as stated in the problem.  
   - Total Others applications = $$ 2 	imes 20 = 40 $$.

4. **Processing Time for Others Applications:**  
   - Maximum processing time per application for Others is **10 minutes** (as per the problem).

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#### **Calculation of Maximum Total Processing Time:**
1. **Total Processing Time for Others Applications:**  
   $$ 	ext{Total processing time} = 	ext{Total applications} 	imes 	ext{Processing time per application} $$  
   $$ = 40 	imes 10 = 400 	ext{ minutes}. $$

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#### **Conclusion:**
The maximum possible value of the total time required to process all applications in the Others category is **200 minutes**, as each application takes up to **10 minutes**. Thus, the correct answer is **200**.

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