100gm of an aq. solution of sugar contains 40% sugar by mass. How much water should be evaporated get 70% sugar solution by mass?

Options

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

Explanation

To solve the problem, we need to determine how much water should be evaporated from a 100 g sugar solution that initially contains 40% sugar by mass to obtain a solution that has 70% sugar by mass. Let's break it down step by step.

### Step 1: Determine the initial amounts of sugar and water in the solution.
- The solution weighs 100 g and contains 40% sugar by mass.
- Amount of sugar = 40% of 100 g = 40 g
- Amount of water = Total mass - Mass of sugar = 100 g - 40 g = 60 g

### Step 2: Set up the final condition for the solution.
- We want to create a solution that is 70% sugar by mass.
- Let the final mass of the solution after evaporation be \( x \) grams.
- In this final solution, the mass of sugar will still be 40 g (since we are only evaporating water).
- According to the condition for the final solution:
\[ \frac{\text{Mass of sugar}}{\text{Total mass of solution}} = 70\% \]
This can be expressed as:
\[ \frac{40}{x} = 0.70 \]

### Step 3: Solve for the final mass of the solution.
- Rearranging the equation gives:
\[ 40 = 0.70x \]
- Solving for \( x \):
\[ x = \frac{40}{0.70} \approx 57.14 \text{ g} \]

### Step 4: Calculate the amount of water to be evaporated.
- Initially, we had 60 g of water.
- After evaporation, we want the total mass of the solution to be approximately 57.14 g.
- The mass of water in the final solution can be calculated as:
\[ \text{Mass of water} = \text{Final mass} - \text{Mass of sugar} = 57.14 \text{ g} - 40 \text{ g} = 17.14 \text{ g} \]

### Step 5: Determine the amount of water to evaporate.
- The amount of water to be evaporated is:
\[ \text{Water to evaporate} = \text{Initial mass of water} - \text{Final mass of water} = 60 \text{ g} - 17.14 \text{ g} \approx 42.86 \text{ g} \]

### Final Answer:
Approximately 42.86 g of water should be evaporated to obtain a 70% sugar solution by mass.

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