Cost Analysis Calculating Chairs And Petrol Consumption Efficiency

In this article, we will delve into two practical mathematical problems related to cost analysis and consumption efficiency. The first problem involves determining the number of chairs that can be purchased for a given amount, based on the cost of a set of chairs. The second problem explores the distance a car can travel with a specific amount of petrol, given its fuel consumption rate. These types of problems are common in everyday life and require a solid understanding of basic arithmetic and proportional reasoning. Let's explore these problems in detail and break them down step by step.

Problem 1 Calculating the Number of Chairs

Cost analysis is a critical skill in both personal and professional financial management. This problem specifically focuses on the relationship between the cost of goods and the quantity that can be purchased within a budget. Understanding these relationships is crucial for making informed purchasing decisions, whether it's for household items or business inventory. We start with the given information: the cost of 15 chairs is Rs. 5520. Our goal is to find out how many chairs can be purchased for Rs. 9200. To solve this, we need to first determine the cost of a single chair. This can be done by dividing the total cost of the 15 chairs by the number of chairs. Once we know the cost per chair, we can then divide the total budget of Rs. 9200 by this cost to find the number of chairs that can be purchased. This involves two key arithmetic operations: division and the application of proportional reasoning. The problem highlights the importance of breaking down a larger problem into smaller, manageable steps. By first finding the unit cost, we simplify the process of calculating the quantity that can be purchased with a different budget. This approach is widely applicable in various real-life scenarios, such as comparing prices, budgeting, and inventory management. Moreover, the problem subtly introduces the concept of direct proportion. The number of chairs that can be purchased is directly proportional to the amount of money available. This means that if the budget increases, the number of chairs that can be purchased also increases, assuming the cost per chair remains constant. Understanding direct proportion is a fundamental concept in mathematics and has numerous applications in fields such as economics, finance, and engineering. In the following sections, we will provide a detailed step-by-step solution to this problem, illustrating the calculations and reasoning involved. This will not only provide the answer but also offer a clear methodology that can be applied to similar problems in the future. By mastering such calculations, individuals can make more informed financial decisions and manage their resources more effectively. The ability to quickly and accurately determine the cost-quantity relationship is a valuable asset in today's economy. Finally, remember to always double-check your calculations and ensure that the answer makes sense in the context of the problem. For instance, if the calculated number of chairs seems unusually high or low, it might indicate an error in the calculations. Careful review and logical thinking are essential components of problem-solving in mathematics and beyond.

Step-by-step Solution for Chairs Problem

To find the number of chairs that can be purchased for Rs. 9200, we first need to calculate the cost of one chair. Given that 15 chairs cost Rs. 5520, we can determine the cost per chair by dividing the total cost by the number of chairs: Cost per chair = Total cost / Number of chairs Cost per chair = 5520 / 15 Performing this division, we find that the cost per chair is Rs. 368. Now that we know the cost of one chair, we can calculate how many chairs can be purchased for Rs. 9200. To do this, we divide the total budget by the cost per chair: Number of chairs = Total budget / Cost per chair Number of chairs = 9200 / 368 Performing this division, we find that approximately 25 chairs can be purchased. Therefore, with a budget of Rs. 9200, one can purchase 25 chairs, given the cost of 15 chairs is Rs. 5520. This result provides a clear and concise answer to the problem, demonstrating the practical application of basic arithmetic in everyday scenarios. The solution highlights the importance of breaking down complex problems into simpler steps. By first finding the cost per chair, we were able to easily determine the number of chairs that could be purchased with a different budget. This approach is applicable to a wide range of similar problems, such as calculating the cost of items in bulk, comparing prices between different vendors, or budgeting for purchases. Moreover, this problem reinforces the concept of direct proportion. The number of chairs that can be purchased is directly proportional to the budget. This means that if the budget increases, the number of chairs that can be purchased also increases, assuming the cost per chair remains constant. This principle is fundamental in many areas of mathematics and economics and is crucial for understanding relationships between different quantities. In practical terms, this calculation can help individuals and businesses make informed purchasing decisions. Knowing the cost per unit allows for accurate budgeting and comparison of prices, ensuring that resources are used efficiently. Additionally, understanding the relationship between cost and quantity can aid in negotiating prices and securing better deals. Finally, it is always a good practice to double-check the calculations and ensure that the answer makes sense in the context of the problem. In this case, we found that 25 chairs can be purchased for Rs. 9200, which is a reasonable number given the cost of 15 chairs at Rs. 5520. This logical check helps to avoid errors and ensures the accuracy of the solution.

Problem 2 Petrol Consumption Efficiency

Petrol consumption efficiency is a crucial aspect of vehicle ownership and operation. This problem addresses the relationship between the amount of petrol consumed and the distance a car can travel. Understanding fuel efficiency is not only important for budgeting and cost management but also for environmental considerations. A car consumes 12 litres of petrol in covering a distance of 234 km. The question is: How many kilometres can it run in 26 litres of petrol? This problem requires us to determine the car's fuel consumption rate, which is the distance it can travel per litre of petrol. To find this, we divide the distance covered by the amount of petrol consumed. Once we know the distance per litre, we can then multiply this by the new amount of petrol (26 litres) to find the total distance the car can travel. This problem illustrates the concept of proportional reasoning and the relationship between distance, fuel consumption, and fuel efficiency. It also highlights the practical application of mathematical skills in real-life scenarios. Understanding fuel efficiency can help drivers make informed decisions about vehicle usage, route planning, and fuel purchases. In addition to the mathematical aspects, fuel efficiency has significant environmental implications. Vehicles with better fuel efficiency consume less petrol, which in turn reduces emissions of greenhouse gases and other pollutants. Therefore, understanding and optimizing fuel efficiency is essential for promoting sustainable transportation practices. The problem also subtly introduces the concept of direct proportion. The distance a car can travel is directly proportional to the amount of petrol it has, assuming the fuel consumption rate remains constant. This means that if the amount of petrol doubles, the distance the car can travel also doubles. This relationship is crucial for estimating the range of a vehicle based on its fuel tank capacity and fuel consumption rate. In the following sections, we will provide a detailed step-by-step solution to this problem, demonstrating the calculations and reasoning involved. This will not only provide the answer but also offer a clear methodology that can be applied to similar problems in the future. By mastering such calculations, individuals can make more informed decisions about vehicle usage and fuel management. Furthermore, understanding fuel efficiency can lead to significant cost savings over time. By choosing fuel-efficient vehicles and driving habits, individuals can reduce their petrol expenses and contribute to a more sustainable environment. Finally, remember to always consider other factors that can affect fuel efficiency, such as driving speed, road conditions, and vehicle maintenance. These factors can influence the actual distance a car can travel on a given amount of petrol. Careful monitoring and adjustments can help optimize fuel efficiency and reduce overall transportation costs.

Step-by-step Solution for Petrol Consumption

To determine how many kilometres the car can run in 26 litres of petrol, we first need to calculate the car's fuel consumption rate. Given that the car consumes 12 litres of petrol in covering a distance of 234 km, we can find the distance it can travel per litre by dividing the total distance by the amount of petrol consumed: Distance per litre = Total distance / Petrol consumed Distance per litre = 234 / 12 Performing this division, we find that the car can travel 19.5 km per litre of petrol. Now that we know the distance the car can travel per litre, we can calculate the total distance it can cover with 26 litres of petrol. To do this, we multiply the distance per litre by the total amount of petrol: Total distance = Distance per litre * Petrol available Total distance = 19.5 * 26 Performing this multiplication, we find that the car can travel 507 km with 26 litres of petrol. Therefore, the car can run 507 kilometres in 26 litres of petrol, given its consumption rate of 12 litres for 234 km. This solution provides a clear and concise answer to the problem, demonstrating the practical application of basic arithmetic in calculating fuel efficiency and range. The solution highlights the importance of understanding the relationship between fuel consumption, distance, and fuel efficiency. By first determining the distance the car can travel per litre, we were able to easily calculate the total distance it could cover with a different amount of petrol. This approach is applicable to a wide range of similar problems, such as estimating the range of a vehicle, comparing the fuel efficiency of different vehicles, or planning a road trip. Moreover, this problem reinforces the concept of direct proportion. The distance a car can travel is directly proportional to the amount of petrol it has, assuming the fuel consumption rate remains constant. This means that if the amount of petrol increases, the distance the car can travel also increases. This principle is fundamental in many areas of mathematics and physics and is crucial for understanding relationships between different quantities. In practical terms, this calculation can help drivers make informed decisions about fuel purchases and route planning. Knowing the fuel efficiency of a vehicle allows for accurate estimation of fuel costs and the ability to determine the feasibility of long-distance travel. Additionally, understanding fuel consumption rates can aid in optimizing driving habits to improve fuel efficiency and reduce emissions. Finally, it is always a good practice to double-check the calculations and ensure that the answer makes sense in the context of the problem. In this case, we found that the car can travel 507 km with 26 litres of petrol, which is a reasonable distance given its consumption rate of 12 litres for 234 km. This logical check helps to avoid errors and ensures the accuracy of the solution.

In conclusion, both problems demonstrate the practical application of basic mathematical principles in everyday situations. The first problem illustrated how to calculate the number of items that can be purchased with a given budget, while the second problem demonstrated how to determine the distance a vehicle can travel based on its fuel consumption rate. These types of calculations are essential for making informed decisions in personal finance, transportation, and various other aspects of life. By understanding and applying these mathematical concepts, individuals can effectively manage their resources and plan for the future.