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Understanding sugar solution is crucial in the context of dilution. Let's break it down easily. A sugar solution is essentially a mixture where sugar is the solute and water is the solvent. This mixture can vary in how much sugar it contains, which we refer to as its concentration. In this exercise, we're focusing on how to alter this concentration by adding more water—which is a common task in chemistry and everyday life. When we dilute a sugar solution, we decrease its concentration by adding more water. This means there's less sugar per unit of water. Imagine you're making lemonade: if you add more water to your mix, it tastes less sweet because the concentration of sugar is lower. This same principle applies with the sugar solution in the exercise. When one-fourth of the original sugar solution is poured out to form a new solution and then diluted with water, we effectively reduce the sugar content in the new solution, changing its concentration.

The concentration ratio is a measure of how much sugar is present in each part of the solution. Think of it as a comparison of sweetness if you prefer. In our problem, we're looking at the concentration of sugar before and after dilution. In Solution A, the concentration is defined as the amount of sugar per volume, given by the formula: \[\text{Concentration} = \frac{\text{mass of sugar}}{\text{volume of solution}}\] Given that Solution B has the same mass of sugar but a larger volume due to the added water, the concentration decreases. The exercise asks us to compare these concentration ratios. Surprisingly, the calculation shows that the concentration of sugar in both solutions remains the same after diluting Solution B (1:1 ratio). This is because Solution B has the same proportional amount of sugar per volume as Solution A.

Volume comparison is a determining factor when we talk about dilution, impacting how concentrated a solution is. To understand this, picture the act of pouring one-fourth of a container of sugar water into a new container and adding an equivalent amount of water. Solution A originally had a volume denoted as \( V_A \). When forming Solution B, only one-fourth of Solution A is used, so its initial volume is \( \frac{1}{4} V_A \). After water is added in the same quantity, the volume of Solution B becomes \( \frac{1}{4} V_A + \frac{1}{4} V_A = \frac{1}{2} V_A \). Comparatively, Solution A with its full volume \( V_A \) is four times larger than the volume of diluted Solution B. Hence, the comparison of their volumes after dilution shows a ratio of 4:1 for Solution A to Solution B. This change highlights how dilution impacts not only concentration but also practical aspects like how much space the solution occupies.