Notebook And Diary Pricing Analysis Calculating Selling Price Of 7 Notebooks
In the realm of business, particularly in the retail sector, understanding pricing strategies is paramount. The ability to accurately determine cost prices, selling prices, and profit margins can significantly impact a business's financial health. This article delves into a complex pricing scenario involving notebooks and diaries, meticulously analyzing the relationships between their costs, selling prices, and profit margins. We will dissect the given problem, systematically calculate the unknowns, and ultimately determine the selling price of seven notebooks. This detailed exploration serves as a practical exercise in applying fundamental business principles and enhances our comprehension of pricing dynamics.
The core of our investigation lies in deciphering the intricate relationships between the cost price and selling price of notebooks and diaries. We are presented with a scenario where the loss incurred from selling 18 notebooks is equivalent to the profit gained from selling 6 notebooks. This initial condition provides a crucial foundation for establishing a relationship between the cost price and selling price of a single notebook. Furthermore, the problem introduces the concept of a diary, whose cost price is 50% higher than that of a notebook. This introduces another variable into the equation, requiring us to carefully consider the relative costs of these two products. The diary is then sold at a 30% profit, and its selling price is given as Rs. 390. This information allows us to work backward, calculating the cost price of the diary and subsequently the cost price of a notebook. Armed with this knowledge, we can finally determine the selling price of a notebook and ultimately calculate the selling price of seven notebooks. This step-by-step approach underscores the importance of breaking down complex problems into manageable components, a valuable skill in any business context.
The ultimate goal of this analysis is not merely to arrive at a numerical answer but to gain a deeper understanding of the principles underlying pricing decisions. By meticulously working through the problem, we can appreciate the interconnectedness of cost price, selling price, and profit margin. We will also encounter the concept of loss, which is an equally important consideration in business. Understanding how to calculate and manage losses is crucial for maintaining profitability and ensuring long-term sustainability. This exercise also highlights the importance of clear and organized problem-solving. By systematically approaching the problem, we can avoid confusion and ensure accuracy. The skills and insights gained from this analysis are applicable to a wide range of business scenarios, making it a valuable learning experience for anyone interested in the world of commerce.
The problem states that the selling price of 6 notebooks equals the loss incurred by selling 18 notebooks. This seemingly simple statement holds the key to unlocking the relationship between the cost price and selling price of a single notebook. To unravel this puzzle, let's introduce some notation. Let 'CP' represent the cost price of one notebook and 'SP' represent the selling price of one notebook. The loss incurred on selling one notebook is the difference between the cost price and the selling price, which can be expressed as CP - SP. Therefore, the total loss incurred on selling 18 notebooks is 18(CP - SP). The problem also states that the selling price of 6 notebooks is equal to 6SP. According to the given condition, these two quantities are equal. Therefore, we can write the equation:
6SP = 18(CP - SP)
This equation is the cornerstone of our analysis. It mathematically represents the relationship described in the problem statement. To solve for the unknowns, we need to simplify this equation. We can start by dividing both sides of the equation by 6:
SP = 3(CP - SP)
Next, we distribute the 3 on the right side of the equation:
SP = 3CP - 3SP
Now, we want to isolate the terms involving SP on one side of the equation. We can add 3SP to both sides:
4SP = 3CP
This equation establishes a direct relationship between the selling price (SP) and the cost price (CP) of a notebook. It tells us that four times the selling price is equal to three times the cost price. This is a crucial piece of information that we will use later to determine the actual values of CP and SP.
To further illustrate the significance of this equation, we can rearrange it to express SP in terms of CP:
SP = (3/4)CP
This equation tells us that the selling price of a notebook is 75% of its cost price. This implies that the seller is incurring a loss on each notebook sold, which is consistent with the problem statement. This understanding is crucial for making informed pricing decisions in a business context. We have successfully decoded the initial puzzle, establishing a clear relationship between the cost price and selling price of a notebook.
Now that we have established a relationship between the cost price and selling price of a notebook, let's turn our attention to the diary. The problem states that the cost price of a diary is 50% more than that of a notebook. This provides us with a direct link between the cost prices of the two products. Let's denote the cost price of a diary as CP_diary. According to the problem, CP_diary is 50% more than CP, the cost price of a notebook. We can express this mathematically as:
CP_diary = CP + 0.50CP
Simplifying this equation, we get:
CP_diary = 1.50CP
This equation tells us that the cost price of a diary is 1.5 times the cost price of a notebook. This is a crucial piece of information that will help us determine the actual cost prices of both products.
The problem further states that the diary is sold at a 30% profit, and its selling price is Rs. 390. This provides us with enough information to calculate the cost price of the diary. Let's denote the selling price of the diary as SP_diary. We know that SP_diary = Rs. 390. The profit on the diary is 30% of its cost price, which can be expressed as 0.30CP_diary. The selling price is the sum of the cost price and the profit. Therefore, we can write the equation:
SP_diary = CP_diary + 0.30CP_diary
Simplifying this equation, we get:
SP_diary = 1.30CP_diary
We know that SP_diary = Rs. 390. Substituting this value into the equation, we get:
390 = 1.30CP_diary
To solve for CP_diary, we divide both sides of the equation by 1.30:
CP_diary = 390 / 1.30
CP_diary = 300
Therefore, the cost price of the diary is Rs. 300. This is a significant milestone in our analysis. We have successfully calculated the cost price of the diary using the information provided about its selling price and profit margin. This value will now allow us to determine the cost price of the notebook.
Having determined the cost price of the diary, we can now leverage the relationship we established earlier to calculate the cost price of the notebook. Recall that we found the equation:
CP_diary = 1.50CP
We know that CP_diary = Rs. 300. Substituting this value into the equation, we get:
300 = 1.50CP
To solve for CP, we divide both sides of the equation by 1.50:
CP = 300 / 1.50
CP = 200
Therefore, the cost price of the notebook is Rs. 200. This is a crucial piece of information that we have been working towards. Now that we know the cost price of the notebook, we can use the equation we derived earlier to calculate its selling price:
SP = (3/4)CP
Substituting CP = Rs. 200 into the equation, we get:
SP = (3/4) * 200
SP = 150
Therefore, the selling price of the notebook is Rs. 150. This is another significant milestone in our analysis. We have successfully calculated both the cost price and the selling price of the notebook. This information is crucial for answering the final question posed in the problem.
We have meticulously worked through the intricate relationships between the cost prices and selling prices of notebooks and diaries. By systematically breaking down the problem into smaller components and applying fundamental business principles, we have successfully calculated the unknowns. This process highlights the importance of clear and organized problem-solving in a business context. The ability to accurately determine cost prices, selling prices, and profit margins is essential for making informed business decisions.
The final step in our analysis is to determine the selling price of seven notebooks. We have already calculated the selling price of one notebook to be Rs. 150. To find the selling price of seven notebooks, we simply multiply the selling price of one notebook by seven:
Selling price of 7 notebooks = 7 * SP
Selling price of 7 notebooks = 7 * 150
Selling price of 7 notebooks = 1050
Therefore, the selling price of seven notebooks is Rs. 1050. This is the final answer to the problem. We have successfully navigated through the complexities of notebook and diary pricing, meticulously calculating each unknown and ultimately arriving at the desired solution.
This exercise underscores the importance of understanding pricing dynamics in a business context. By carefully analyzing the relationships between cost prices, selling prices, and profit margins, we can make informed decisions that contribute to the financial health of a business. The skills and insights gained from this analysis are applicable to a wide range of business scenarios, making it a valuable learning experience for anyone interested in the world of commerce. We have demonstrated the power of systematic problem-solving and the importance of breaking down complex problems into manageable components. This approach allows us to avoid confusion and ensure accuracy, ultimately leading to successful outcomes.
In conclusion, this comprehensive analysis of notebook and diary pricing has provided valuable insights into the intricacies of business calculations. We successfully determined the selling price of seven notebooks by meticulously dissecting the problem, establishing relationships between cost prices and selling prices, and applying fundamental business principles. This exercise has highlighted the importance of clear and organized problem-solving, the ability to translate word problems into mathematical equations, and the significance of understanding pricing dynamics in a business context. The skills and insights gained from this analysis are applicable to a wide range of business scenarios, making it a valuable learning experience for anyone interested in the world of commerce. The final answer, the selling price of seven notebooks, is Rs. 1050, a testament to our meticulous calculations and systematic approach. This analysis serves as a practical example of how mathematical concepts can be applied to real-world business problems, fostering a deeper understanding of the interplay between numbers and commerce.