Solving Sales Puzzle Determining Transaction Price Between A And B

In the realm of business transactions, understanding the concept of value added is crucial for assessing the economic contribution of each participant in the supply chain. This article delves into a specific scenario involving three entities – A, B, and C – to illustrate how value added is calculated and how it impacts the final price of a product. Let's dissect the problem and arrive at the solution, ensuring a clear understanding of the underlying economic principles.

H2: The Sales Scenario A to B to C

Our scenario involves a sequence of sales transactions. Entity A produces a certain output and sells it entirely to entity B. Subsequently, entity B processes this output further and sells it to entity C for Rs 60. The core of the problem lies in the statement: B's value added is equal to A's. This provides the critical piece of information we need to determine the price at which A sold its output to B. To solve this, we need to understand the concept of value added and how it's calculated. Value added is the incremental wealth created by a business. It represents the difference between the value of the goods or services a company produces (its output) and the cost of the inputs it uses to produce those goods or services. In simpler terms, it's the extra value a business adds to the raw materials or components it purchases before selling the finished product.

In this specific case, entity A's value added is the value of its output since it's assumed that A doesn't have any intermediate consumption. For instance, if A is a wheat farmer, the value added by A would be the market value of the wheat produced. Entity B, on the other hand, buys the output from A, adds its own processing or manufacturing steps, and then sells the final product to C. B's value added is the difference between the price B receives from C and the price B paid to A. If B is a flour mill, then B adds value by converting wheat (purchased from A) into flour. This added value covers B's costs (labor, electricity, etc.) and contributes to its profit.

Consider this example: If A sells wheat to B for Rs 20, and B converts it into flour and sells it to C for Rs 60, B's value added would be Rs 60 - Rs 20 = Rs 40. The problem states that B's value added is equal to A's value added. This is a critical piece of information that lets us set up an equation. If we denote the price at which A sells to B as 'x', then A's value added is 'x'. B's value added is the selling price to C (Rs 60) minus the price B paid to A ('x'). So, we have the equation: B's Value Added = Rs 60 - x. The problem states that B's value added is equal to A's value added, so we can set up the equation: x = 60 - x. Solving this equation will give us the value of 'x', which is the price at which A sold its output to B.

H2: Deconstructing Value Added The Key to Solving the Problem

To effectively address this problem, we must first solidify our grasp on the concept of value added. It's not merely a financial term; it's a reflection of the economic contribution an entity makes in a production process. Consider it as the 'extra something' a business brings to the table, transforming raw materials or semi-finished goods into something more valuable. Value added bridges the gap between the cost of inputs and the revenue generated from outputs. The formula for calculating value added is straightforward: Value Added = Revenue from Sales - Cost of Intermediate Goods. Intermediate goods are the inputs a business uses in its production process – raw materials, components, or services purchased from other businesses. Think of a furniture manufacturer. They buy wood, fabric, and other materials (intermediate goods), transform them into furniture, and then sell the furniture. The revenue from furniture sales minus the cost of wood, fabric, and other materials gives the value added by the furniture manufacturer.

In our scenario, A's value added is relatively simple to understand. Since A sells its entire output to B, A's value added is simply the price at which it sells to B. We are assuming that A has no other intermediate costs in this simplified model. If A were a wheat farmer, the value added would be the market value of the wheat when sold. B's value added is a bit more complex, but follows the same principle. B purchases the output from A, adds its own labor, machinery, and other inputs to process the output further, and then sells the finished product to C. The price B receives from C represents the total value of the product after B's contribution. To calculate B's value added, we subtract the cost of the output purchased from A from the price B receives from C. This difference represents the value B has added to the product. Let’s illustrate with an example. Suppose A sells cotton to B for Rs 30, and B turns it into fabric and sells it to C for Rs 80. B's value added would be Rs 80 (sales revenue) - Rs 30 (cost of cotton) = Rs 50. This means B has added Rs 50 of value through its processing and manufacturing activities.

The condition that B's value added is equal to A's is the key to solving the problem. This equality allows us to set up an algebraic equation. Let's denote the price at which A sells to B as 'x'. According to the problem, A's value added is 'x'. B's value added is the selling price to C (Rs 60) minus the price B paid to A ('x'). Thus, B's value added is '60 - x'. Since A's value added is equal to B's value added, we have the equation: x = 60 - x. Solving this equation involves simple algebraic manipulation. Add 'x' to both sides of the equation: x + x = 60 - x + x, which simplifies to 2x = 60. Now, divide both sides by 2: 2x / 2 = 60 / 2, which gives us x = 30. Therefore, A sells its output to B for Rs 30. This is the solution to our problem.

H2: The Algebraic Solution Cracking the Code

The core of solving this problem lies in translating the word problem into an algebraic equation. This approach allows us to use the power of mathematics to find the unknown value – the price at which A sells to B. Let's break down the process step-by-step to ensure clarity and understanding. The key piece of information is the statement: ***