100gm of an aq. solution of sugar contains 40% sugar by mass. How much water should be evaporated get 60% sugar solution by mass?

Explanation

To solve the problem step by step, we need to determine how much water should be evaporated from a 100 g sugar solution that initially contains 40% sugar by mass in order to achieve a final solution that contains 60% sugar by mass.

### Step 1: Determine the initial amounts of sugar and water in the solution.
- The total mass of the solution is given as 100 g.
- The mass percentage of sugar is 40%. Therefore, the mass of sugar in the solution can be calculated as:
\[ \text{Mass of sugar} = \frac{40}{100} \times 100 \text{ g} = 40 \text{ g} \]
- The mass of water in the solution can be calculated as:
\[ \text{Mass of water} = 100 \text{ g} - \text{Mass of sugar} = 100 \text{ g} - 40 \text{ g} = 60 \text{ g} \]

### Step 2: Set up the final condition for the solution.
- We want to achieve a solution that is 60% sugar by mass. Let \( x \) be the mass of water that needs to be evaporated.
- After evaporation, the mass of the solution will be:
\[ \text{Final mass of solution} = \text{Mass of sugar} + \text{Mass of remaining water} = 40 \text{ g} + (60 \text{ g} - x) \]
- The final mass of the solution can be expressed as:
\[ \text{Final mass of solution} = 40 \text{ g} + 60 \text{ g} - x = 100 \text{ g} - x \]

### Step 3: Set up the equation for the final concentration of sugar.
- For the final solution to be 60% sugar by mass, we can set up the equation:
\[ \frac{\text{Mass of sugar}}{\text{Final mass of solution}} = 0.60 \]
Substituting the known values:
\[ \frac{40 \text{ g}}{100 \text{ g} - x} = 0.60 \]

### Step 4: Solve the equation for \( x \).
- Cross-multiplying gives:
\[ 40 = 0.60 \times (100 - x) \]
- Expanding the right side:
\[ 40 = 60 - 0.60x \]
- Rearranging the equation:
\[ 0.60x = 60 - 40 \]
\[ 0.60x = 20 \]
- Dividing both sides by 0.60:
\[ x = \frac{20}{0.60} = \frac{200}{6} \approx 33.33 \text{ g} \]

### Step 5: Conclusion
- Therefore, the amount of water that should be evaporated to achieve a 60% sugar solution is approximately **33.33 g**.