Calculating The Cost Of One Showpiece If A Dozen Cost ₹ 230
In the realm of everyday mathematics, we often encounter scenarios where we need to determine the unit cost of an item given the cost of a bulk quantity. This is a fundamental skill applicable in various situations, from grocery shopping to managing household budgets. In this article, we will delve into a specific problem: If the cost of a dozen showpieces is ₹ 230, what will be the cost of one showpiece? We will explore the underlying concepts, provide a step-by-step solution, and discuss the importance of understanding unit costs in practical life.
Before diving into the solution, let's break down the problem statement. We are given that the cost of a dozen showpieces is ₹ 230. A dozen is a collective term representing 12 items. Therefore, we know that 12 showpieces cost ₹ 230. Our goal is to find the cost of a single showpiece. This involves dividing the total cost by the number of showpieces. The concept we will use here is the unitary method, a basic yet powerful tool in arithmetic.
The unitary method is a technique used to find the value of a single unit and then use that value to find the value of any number of units. In our case, the unit is a single showpiece. By finding the cost of one showpiece, we can then easily calculate the cost of any number of showpieces. This method is particularly useful in solving problems related to ratios, proportions, and rates. Understanding the unitary method not only helps in solving mathematical problems but also enhances our ability to make informed decisions in everyday life. For instance, when comparing prices of different products sold in varying quantities, the unitary method allows us to determine which product offers the best value for money. Moreover, this method is a cornerstone in more advanced mathematical concepts such as direct and inverse proportions, making it an essential skill to master.
To find the cost of one showpiece, we need to divide the total cost (₹ 230) by the number of showpieces (12). This can be represented mathematically as:
Cost of one showpiece = Total cost / Number of showpieces
Plugging in the values, we get:
Cost of one showpiece = ₹ 230 / 12
Now, we perform the division:
₹ 230 ÷ 12 = ₹ 19.1666...
Since we are dealing with currency, it is practical to round the result to two decimal places. Therefore, the cost of one showpiece is approximately ₹ 19.17.
This calculation demonstrates a simple yet crucial application of division in real-world scenarios. The ability to divide and find unit costs is invaluable in various situations, such as budgeting, shopping, and financial planning. Furthermore, understanding the process of rounding decimals is essential in ensuring accuracy and practicality in financial calculations. Rounding to two decimal places is standard practice when dealing with currency, as it represents the nearest cent or paisa. In this case, rounding ₹ 19.1666... to ₹ 19.17 provides a precise and usable figure for the cost of one showpiece. This step-by-step approach not only solves the problem at hand but also reinforces the importance of precision and attention to detail in mathematical computations. Moreover, it highlights how basic arithmetic operations can be applied to solve practical problems, making mathematics relevant and accessible in everyday contexts.
As mentioned earlier, we used the unitary method to solve this problem. Let's revisit the concept to solidify our understanding. The unitary method involves first finding the value of a single unit (in this case, one showpiece) and then using that value to calculate the cost of any number of units.
In our problem, we know the cost of 12 showpieces. To find the cost of one showpiece, we divide the total cost by 12. This gives us the unit cost. Once we have the unit cost, we can easily determine the cost of any number of showpieces by multiplying the unit cost by the desired quantity.
The unitary method is a versatile technique that can be applied to a wide range of problems. For instance, if we wanted to find the cost of 5 showpieces, we would simply multiply the unit cost (₹ 19.17) by 5. This would give us:
Cost of 5 showpieces = ₹ 19.17 * 5 = ₹ 95.85
The beauty of the unitary method lies in its simplicity and adaptability. It allows us to break down complex problems into manageable steps, making it easier to find the solution. This method is particularly useful in scenarios involving direct proportion, where an increase in one quantity results in a proportional increase in another quantity. For example, if the number of showpieces increases, the total cost also increases proportionally. Understanding and mastering the unitary method is not only beneficial in mathematical problem-solving but also in developing critical thinking and analytical skills that are valuable in various aspects of life. It empowers individuals to make informed decisions, compare values, and solve practical problems efficiently.
Understanding unit costs is crucial in various real-life scenarios. It allows us to make informed decisions when purchasing goods, managing budgets, and comparing prices. Here are some key reasons why understanding unit costs is important:
1. Informed Purchasing Decisions: When shopping, we often encounter products sold in different quantities and at varying prices. By calculating the unit cost, we can determine which product offers the best value for money. For example, a larger package might have a lower price per unit compared to a smaller package, even though the total cost is higher.
2. Budget Management: Understanding unit costs helps in effective budget management. By knowing the cost of individual items, we can track our spending more accurately and identify areas where we can save money. This is particularly useful when planning household expenses or managing personal finances. For instance, knowing the unit cost of groceries allows us to compare prices across different stores and make budget-friendly choices. Similarly, understanding the unit cost of utilities like electricity or water helps in monitoring consumption and identifying potential cost-saving measures.
3. Price Comparison: Unit cost calculation is essential for comparing prices of similar products from different brands or vendors. Without knowing the unit cost, it can be challenging to determine which product is the most economical choice. This is especially important when making bulk purchases or comparing offers from different suppliers. For example, when buying office supplies or raw materials for a business, calculating unit costs helps in selecting the most cost-effective options. This ensures that the business operates efficiently and maximizes its profitability.
4. Waste Reduction: Understanding unit costs can also contribute to waste reduction. By knowing the cost of individual items, we are more likely to use them judiciously and avoid wastage. This is particularly relevant in areas such as food consumption and resource utilization. For example, understanding the cost per serving of a particular food item can encourage us to prepare meals in appropriate quantities, reducing food waste. Similarly, knowing the unit cost of resources like water or energy can motivate us to conserve them and minimize unnecessary consumption.
In summary, understanding unit costs empowers us to make smarter financial decisions, manage our resources effectively, and avoid unnecessary expenses. It is a fundamental skill that contributes to financial literacy and overall economic well-being.
The concept of unit cost is applicable in numerous real-world situations. Let's explore some examples:
1. Grocery Shopping: Imagine you are at the supermarket and want to buy cereal. There are two options: a small box containing 10 ounces for ₹ 150 and a large box containing 18 ounces for ₹ 250. To determine which is the better deal, you need to calculate the unit cost (cost per ounce) for each box.
For the small box:
Unit cost = ₹ 150 / 10 ounces = ₹ 15 per ounce
For the large box:
Unit cost = ₹ 250 / 18 ounces = ₹ 13.89 per ounce (approximately)
In this case, the large box is the better deal as it has a lower unit cost.
2. Bulk Purchases: Businesses often make bulk purchases to save money. However, it's essential to calculate the unit cost to ensure that the bulk purchase is indeed cost-effective. For example, a company might buy paper in reams or boxes. By calculating the cost per sheet, they can compare prices from different suppliers and choose the most economical option. This ensures that the company optimizes its purchasing decisions and minimizes expenses.
3. Fuel Efficiency: Understanding unit costs is also relevant in assessing fuel efficiency. If you know the price of fuel per liter and the fuel consumption of your vehicle, you can calculate the cost per kilometer or mile. This helps in comparing the fuel efficiency of different vehicles or evaluating the cost of travel for various routes. For instance, if you are planning a road trip, calculating the fuel cost per kilometer can help you estimate the total fuel expenses and make informed decisions about travel routes and modes of transportation.
4. Manufacturing Costs: In manufacturing, unit cost calculation is crucial for determining the profitability of a product. By knowing the cost of raw materials, labor, and overhead expenses, manufacturers can calculate the cost per unit. This information is essential for setting prices, managing production costs, and maximizing profits. Understanding the unit cost also helps in identifying areas where costs can be reduced, such as optimizing production processes or negotiating better deals with suppliers. This ensures that the manufacturing operation remains competitive and financially sustainable.
These examples illustrate the diverse applications of unit cost calculation in real-world scenarios. Whether it's making purchasing decisions, managing business expenses, or assessing fuel efficiency, understanding unit costs is a valuable skill that contributes to financial literacy and effective decision-making.
In conclusion, determining the cost of one showpiece when a dozen cost ₹ 230 is a straightforward mathematical problem that highlights the importance of understanding unit costs. By dividing the total cost by the number of items, we found that one showpiece costs approximately ₹ 19.17. This exercise underscores the practical application of basic arithmetic in everyday life. Understanding unit costs is crucial for making informed purchasing decisions, managing budgets effectively, and comparing prices accurately. Whether you are shopping for groceries, planning a budget, or managing a business, the ability to calculate unit costs empowers you to make smarter financial decisions. The unitary method, as demonstrated in this article, is a versatile tool that can be applied to a wide range of problems, making it an essential skill for anyone seeking to enhance their financial literacy and problem-solving abilities. By mastering these fundamental concepts, individuals can navigate the complexities of the financial world with greater confidence and competence.
