100gm of an aq. solution of sugar contains 50% sugar by mass. How much water should be evaporated get 80% sugar solution by mass?

Options

A. 10g
B. 20g
C. 30g
D. None of these

Explanation

To solve the problem, we need to determine how much water must be evaporated from a 100g sugar solution that initially contains 50% sugar by mass in order to achieve an 80% sugar solution by mass.

### Step-by-Step Solution:

1. **Identify the initial composition of the solution:**
- The total mass of the solution = 100 g
- The mass of sugar = 50% of 100 g = 50 g
- The mass of water = 100 g - 50 g = 50 g

2. **Determine the final composition required:**
- We want an 80% sugar solution by mass.
- In an 80% sugar solution, if we denote the final mass of the solution as \( x \), then:
- Mass of sugar = 80% of \( x \) = 0.8x
- Mass of water = 20% of \( x \) = 0.2x

3. **Set up the equation based on the mass of sugar:**
- The mass of sugar remains constant during evaporation, so:
- 0.8x = 50 g (since the mass of sugar does not change)
- Solving for \( x \):
\[ x = \frac{50}{0.8} = 62.5 \text{ g} \]

4. **Calculate the mass of water in the final solution:**
- Mass of water in the final solution = 20% of \( x \):
\[ \text{Mass of water} = 0.2 \times 62.5 = 12.5 \text{ g} \]

5. **Determine the amount of water that needs to be evaporated:**
- Initial mass of water = 50 g
- Final mass of water = 12.5 g
- Therefore, the mass of water to be evaporated:
\[ \text{Water evaporated} = 50 \text{ g} - 12.5 \text{ g} = 37.5 \text{ g} \]

### Final Answer:
To achieve an 80% sugar solution by mass, **37.5 grams of water should be evaporated.**

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