Sports Academy Admission Eligibility Based On Distance A Practical Problem

The question is whether Tarun, Vivek, and Riya are eligible for admission to the sports academy based on the distance from their home to the academy. Tarun lives 3,000 meters away, Vivek lives 82,000 decimeters away, and Riya lives 600,000 centimeters away. The academy only accepts students who live within 8 km of the academy.

In this article, we delve into a practical problem involving distance measurements and eligibility criteria for admission to a sports academy. The scenario presents three individuals – Tarun, Vivek, and Riya – who are vying for a spot in a sports academy. However, there's a crucial condition: the academy exclusively admits students residing within an 8-kilometer radius. Our task is to meticulously analyze the distances of each applicant's residence from the academy, ensuring that all measurements are converted to a uniform unit, and subsequently ascertain whether they meet the academy's geographical eligibility criteria. This exercise underscores the importance of unit conversions and comparative analysis in real-world applications, particularly in scenarios involving spatial constraints and admissions processes.

Distance and Admission Criteria are crucial factors in determining eligibility. Tarun, Vivek, and Riya's applications hinge on their proximity to the academy. The academy's rule is clear: only those living within 8 kilometers are eligible. This immediately introduces the concept of a threshold – a maximum permissible distance. To assess their eligibility, we must first express all distances in a common unit. This is where unit conversion becomes paramount. Tarun's distance is given in meters, Vivek's in decimeters, and Riya's in centimeters. To make a fair comparison, we need to convert all these measurements to kilometers, which is the unit specified in the academy's criteria. This conversion process isn't just a mathematical exercise; it's a practical step in ensuring accurate evaluation and decision-making.

Unit conversion is the cornerstone of solving this problem. To accurately compare the distances, we must convert all measurements into a single, consistent unit – kilometers. This involves understanding the relationships between different metric units.

• Meters to Kilometers: There are 1,000 meters in a kilometer. To convert meters to kilometers, we divide the number of meters by 1,000. For Tarun, who lives 3,000 meters away, this conversion is essential to determine his distance in relation to the 8-kilometer limit.
• Decimeters to Kilometers: There are 10 decimeters in a meter and 1,000 meters in a kilometer. Therefore, there are 10,000 decimeters in a kilometer. To convert decimeters to kilometers, we divide the number of decimeters by 10,000. Vivek's distance, given in decimeters, requires this conversion to assess his eligibility.
• Centimeters to Kilometers: There are 100 centimeters in a meter and 1,000 meters in a kilometer. This means there are 100,000 centimeters in a kilometer. To convert centimeters to kilometers, we divide the number of centimeters by 100,000. Riya's distance, provided in centimeters, must undergo this conversion for a fair evaluation.

This conversion process is not merely about applying formulas; it's about creating a common ground for comparison. Once all distances are in kilometers, we can directly compare them to the academy's 8-kilometer limit and make informed decisions about each applicant's eligibility. The accuracy of these conversions is paramount, as even a small error could lead to an incorrect determination.

Now, let's apply these conversion factors to the distances of Tarun, Vivek, and Riya, expressing each in kilometers. This step is crucial for determining whether each applicant meets the academy's eligibility criteria based on their proximity.

1. Tarun's Distance: Tarun lives 3,000 meters away from the academy. To convert this distance to kilometers, we divide by 1,000:

   3,000 meters / 1,000 = 3 kilometers

   This calculation shows that Tarun lives 3 kilometers from the academy, a crucial piece of information for assessing his eligibility.

2. Vivek's Distance: Vivek's residence is 82,000 decimeters from the academy. To convert this to kilometers, we divide by 10,000:

   82,000 decimeters / 10,000 = 8.2 kilometers

   This result indicates that Vivek lives 8.2 kilometers away, which will be compared against the academy's limit.

3. Riya's Distance: Riya lives 600,000 centimeters away from the sports academy. Converting this to kilometers involves dividing by 100,000:

   600,000 centimeters / 100,000 = 6 kilometers

   This calculation places Riya's residence at 6 kilometers from the academy, another key factor in determining her eligibility.

By performing these conversions, we've transformed the initial distances into a common unit, allowing for a direct and meaningful comparison against the academy's 8-kilometer requirement. The next step is to analyze these results and determine which applicants meet the criteria.

With the distances now expressed in kilometers, we can directly assess the eligibility of Tarun, Vivek, and Riya for admission to the sports academy. The academy's rule is clear: applicants must reside within 8 kilometers to be considered.

• Tarun's Eligibility: Tarun lives 3 kilometers from the academy. Since 3 kilometers is less than 8 kilometers, Tarun meets the distance requirement and is eligible for admission. This makes Tarun a strong candidate from a geographical standpoint.
• Vivek's Eligibility: Vivek lives 8.2 kilometers away from the academy. This distance exceeds the 8-kilometer limit. Therefore, Vivek does not meet the academy's distance criteria and is, unfortunately, ineligible for admission based on this factor. Vivek's case highlights the importance of adhering to specified limits in admissions processes.
• Riya's Eligibility: Riya's residence is 6 kilometers from the academy. As 6 kilometers is less than 8 kilometers, Riya satisfies the distance requirement and is eligible for admission. Riya, like Tarun, is geographically well-suited for the academy.

This eligibility determination is a direct result of the accurate unit conversions and comparisons we performed. It demonstrates how a clear understanding of measurement units and their relationships is crucial for making informed decisions in practical scenarios. The outcome underscores the academy's commitment to its geographical criteria and the importance of these criteria in the admissions process.

In conclusion, this problem illustrates the practical application of unit conversions and distance calculations in a real-world scenario. By converting the distances of Tarun, Vivek, and Riya from meters, decimeters, and centimeters to kilometers, we were able to accurately assess their eligibility for admission to the sports academy. Tarun and Riya, residing within the 8-kilometer radius, meet the academy's criteria, while Vivek, at 8.2 kilometers, does not. This exercise not only reinforces the importance of unit conversions in mathematical problem-solving but also highlights their significance in everyday situations where precise measurements and comparisons are necessary. Understanding and applying these concepts allows for informed decision-making and ensures fairness and accuracy in evaluations, whether in academic admissions or other practical contexts.