100gm of an aq. solution of sugar contains 30% sugar by mass. How much water should be evaporated get 50% sugar solution by mass?

Options

A. 10g
B. 20g
C. 30g
D. 40g

Explanation

To solve the problem step by step, let's break down the information given and calculate how much water needs to be evaporated to achieve a 50% sugar solution by mass.

### Step 1: Determine the initial mass of sugar and water in the solution.
- We know that the solution weighs 100 grams and contains 30% sugar by mass.
- Therefore, the mass of sugar in the solution is:
\[ \text{Mass of sugar} = 30\% \text{ of } 100 \text{ g} = \frac{30}{100} \times 100 \text{ g} = 30 \text{ g} \]
- The mass of water in the solution is:
\[ \text{Mass of water} = 100 \text{ g} - \text{Mass of sugar} = 100 \text{ g} - 30 \text{ g} = 70 \text{ g} \]

### Step 2: Set up the final condition for the solution.
- We want to achieve a solution that is 50% sugar by mass. This means that in the final solution, the mass of sugar should equal the mass of water.
- Let \( x \) be the mass of water that needs to be evaporated. After evaporation, the mass of water will be:
\[ \text{Final mass of water} = 70 \text{ g} - x \]
- The total mass of the solution after evaporation will be:
\[ \text{Final mass of solution} = \text{Mass of sugar} + \text{Final mass of water} = 30 \text{ g} + (70 \text{ g} - x) = 100 \text{ g} - x \]

### Step 3: Set up the equation for the final concentration.
- For the final solution to be 50% sugar by mass, we can set up the equation:
\[ \frac{\text{Mass of sugar}}{\text{Final mass of solution}} = 50\% \]
Substituting the known values:
\[ \frac{30 \text{ g}}{100 \text{ g} - x} = 0.5 \]

### Step 4: Solve for \( x \).
- Cross-multiplying gives:
\[ 30 \text{ g} = 0.5 \times (100 \text{ g} - x) \]
Simplifying:
\[ 30 \text{ g} = 50 \text{ g} - 0.5x \]
Rearranging:
\[ 0.5x = 50 \text{ g} - 30 \text{ g} = 20 \text{ g} \]
Therefore:
\[ x = \frac{20 \text{ g}}{0.5} = 40 \text{ g} \]

### Conclusion
- The amount of water that should be evaporated to achieve a 50% sugar solution by mass is **40 grams**.