A sugar solution contains 15% sugar by weight. When the solution is heated, 40% sugar is left in the solution. What is the amount of water which has disappeared ?

To solve the problem of how much water has evaporated from a sugar solution when heated, we first need to understand the initial conditions and the changes that occur during the heating process. Let's break it down step by step.

Initial Conditions of the Sugar Solution

We start with a sugar solution that contains 15% sugar by weight. This means that for every 100 grams of the solution, there are 15 grams of sugar and 85 grams of water.

Understanding the Heating Effect

When the solution is heated, it is stated that 40% sugar remains in the solution. The key here is to realize that the amount of sugar does not change during heating; rather, it is the concentration that changes due to the evaporation of water.

Finding the Amount of Sugar

Let’s assume we have 100 grams of the initial solution. Using the 15% concentration:

• Sugar = 15 grams
• Water = 85 grams

Calculating the New Concentration

After heating, the solution now contains 40% sugar. We need to find the new total weight of the solution (water + sugar) that results in this concentration. Let’s denote the new total weight of the solution as "x" grams. The amount of sugar remains the same at 15 grams.

Since sugar now represents 40% of the total solution, we can set up the equation:

0.40x = 15

Solving for x gives:

x = 15 / 0.40 = 37.5 grams

Calculating the Amount of Water Lost

Now that we know the new total weight of the solution is 37.5 grams, we can determine how much water has evaporated. Initially, the solution had 100 grams (15 grams of sugar + 85 grams of water). The amount of water in the new solution is:

Water in new solution = Total weight - Sugar = 37.5 grams - 15 grams = 22.5 grams

Final Calculation

To find the amount of water that has disappeared due to heating, we subtract the amount of water remaining from the initial amount:

Amount of water lost = Initial water - Remaining water

Amount of water lost = 85 grams - 22.5 grams = 62.5 grams

Summary of the Results

In conclusion, the total amount of water that has evaporated from the sugar solution when heated is 62.5 grams. This calculation illustrates the relationship between concentration, total solution weight, and the effect of heating on a mixture.