What is the percentage of sugar in the syrup made of 10kg of water and 5kg of sugar?
The correct answer and explanation is:
Correct Answer: 33.33%
Explanation:
To calculate the percentage of sugar in the syrup, first determine the total mass of the mixture. The syrup is made by combining 10 kg of water with 5 kg of sugar. Total mass of syrup=10 kg (water)+5 kg (sugar)=15 kg\text{Total mass of syrup} = 10 \text{ kg (water)} + 5 \text{ kg (sugar)} = 15 \text{ kg}
Next, calculate the proportion of sugar in the total mixture: Percentage of sugar=(Mass of sugarTotal mass of syrup)×100=(515)×100=33.33%\text{Percentage of sugar} = \left( \frac{\text{Mass of sugar}}{\text{Total mass of syrup}} \right) \times 100 = \left( \frac{5}{15} \right) \times 100 = 33.33\%
This means that 33.33% of the total mass of the syrup is sugar.
Understanding this percentage is important in many real-life applications. In food processing and nutrition labeling, knowing the concentration of an ingredient helps in regulating diet and ensuring proper formulation. Syrups with higher sugar concentrations may be used for preservation, flavor enhancement, or sweetness in recipes. On the other hand, lower sugar content may be preferred for health-conscious products.
The percentage tells how concentrated the sugar is in the solution. A 33.33% sugar concentration is considered moderately sweet and is typical for many homemade syrups. If more sugar is added, the concentration will rise, making the syrup thicker and sweeter. Similarly, adding more water would reduce the sugar concentration.
This method of percentage calculation is also used in chemistry, medicine, and industry for making solutions, measuring dosages, and ensuring product consistency. Understanding mass percentages gives a clear idea of the composition of mixtures and helps in quality control and formulation of products.