Calculating The Cost Of One Showpiece If A Dozen Costs ₹ 230

Jul 13, 2025 by Admin 61 views

In this article, we will delve into a simple yet practical mathematical problem: determining the cost of a single showpiece when the cost of a dozen (12) showpieces is known. This type of calculation is fundamental in everyday life, whether you're shopping for groceries or managing a business. Understanding the basics of unit cost calculation is essential for making informed decisions and managing your finances effectively.

The problem we are addressing is as follows: If the cost of a dozen showpieces is ₹ 230, what will be the cost of one showpiece? This problem falls under the category of basic arithmetic and involves the concept of division. To solve it, we need to divide the total cost of the dozen showpieces by the number of showpieces in a dozen.

To solve this problem, we need to understand a few key concepts:

Dozen: A dozen is a group of 12 items. This is a common unit of measurement used for selling and purchasing various items.
Total Cost: The total cost is the overall price paid for a group of items, in this case, a dozen showpieces.
Unit Cost: The unit cost is the price of a single item. This is what we are trying to determine.

The relationship between these concepts can be expressed as follows:

Total Cost = Unit Cost × Number of Items

In our case:

₹ 230 = Unit Cost × 12

To find the cost of one showpiece, we need to isolate the "Unit Cost" in the equation above. We can do this by dividing both sides of the equation by 12:

Unit Cost = ₹ 230 / 12

Now, we perform the division:

₹ 230 ÷ 12 = ₹ 19.1666...

Since we are dealing with currency, we need to round the result to the nearest paisa (two decimal places). Therefore, the cost of one showpiece is approximately ₹ 19.17.

Let's go through the division process in detail:

As we can see, the division results in 19.1666... The repeating decimal indicates that the division is not exact. However, for practical purposes, we round the result to two decimal places to represent the cost in rupees and paisa.

Understanding how to calculate the unit cost is crucial in various real-world scenarios. For example:

Shopping: When buying items in bulk, calculating the unit cost helps you compare prices and determine if you're getting a good deal.
Budgeting: Knowing the cost per item allows you to budget your expenses more accurately.
Business: Businesses use unit cost calculations to determine pricing, profitability, and inventory management.

While division is the most direct method for solving this problem, there are alternative approaches you can use:

Proportion: You can set up a proportion to solve for the unit cost. If 12 showpieces cost ₹ 230, then 1 showpiece will cost x. The proportion can be written as:

12 / 230 = 1 / x

Cross-multiplying, we get:

12x = 230

x = 230 / 12

x = ₹ 19.17 (approximately)
Estimation: You can estimate the unit cost by rounding the numbers. For example, you can round ₹ 230 to ₹ 240 and 12 to 10. Then, divide ₹ 240 by 10 to get an estimated unit cost of ₹ 24. This is just an approximation, but it can give you a quick idea of the cost.

When solving this type of problem, it's important to avoid common mistakes such as:

Incorrect Division: Ensure you perform the division accurately. Double-check your calculations to avoid errors.
Rounding Errors: When rounding the result, make sure you round to the appropriate number of decimal places. For currency, it's usually two decimal places.
Misunderstanding the Problem: Make sure you understand what the problem is asking. In this case, we are looking for the cost of one showpiece, not the total cost of a different number of showpieces.

To reinforce your understanding, here are a few practice problems:

If the cost of 15 pens is ₹ 180, what is the cost of one pen?
If a box of 24 chocolates costs ₹ 480, what is the cost of one chocolate?
If a set of 6 books costs ₹ 750, what is the cost of one book?

Try solving these problems using the methods discussed in this article. This will help you develop your problem-solving skills and build confidence in your ability to handle similar situations.

In conclusion, determining the cost of one item when the cost of a group of items is known is a fundamental mathematical skill. By dividing the total cost by the number of items, we can easily find the unit cost. In the case of the showpieces, the cost of one showpiece is approximately ₹ 19.17 when a dozen costs ₹ 230. This type of calculation is essential for making informed purchasing decisions and managing finances effectively. Understanding and practicing these basic arithmetic principles will empower you to tackle real-world problems with confidence.

Remember, mathematics is not just about formulas and equations; it's a tool for understanding and navigating the world around us. By mastering these basic concepts, you'll be well-equipped to handle a wide range of practical situations.

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