100gm of an aq. solution of sugar contains 40% sugar by mass. How much water should be evaporated get 80% 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 in order to achieve a final solution that contains 80% sugar by mass.

### Step-by-Step Solution:

1. **Determine the initial mass of sugar and water:**
- The solution is 100 g and contains 40% sugar by mass.
- Mass of sugar = 40% of 100 g = 0.40 × 100 g = 40 g
- Mass of water = Total mass - Mass of sugar = 100 g - 40 g = 60 g

2. **Set up the final condition for the desired solution:**
- We want an 80% sugar solution by mass.
- Let \( x \) be the mass of water that needs to be evaporated.
- After evaporation, the mass of water will be \( 60 g - x \).
- The total mass of the new solution will then be \( 40 g + (60 g - x) = 100 g - x \).

3. **Set up the equation for the final concentration:**
- For the final solution to be 80% sugar by mass:
\[ \frac{\text{mass of sugar}}{\text{total mass of solution}} = 0.80 \]
\[ \frac{40 g}{100 g - x} = 0.80 \]

4. **Solve the equation for \( x \):**
- Cross-multiply to eliminate the fraction:
\[ 40 g = 0.80 \times (100 g - x) \]
- Distributing the 0.80:
\[ 40 g = 80 g - 0.80x \]
- Rearranging the equation:
\[ 0.80x = 80 g - 40 g \]
\[ 0.80x = 40 g \]
- Dividing both sides by 0.80:
\[ x = \frac{40 g}{0.80} = 50 g \]

5. **Conclusion:**
- Therefore, the amount of water that should be evaporated to obtain an 80% sugar solution is **50 grams**.

### Final Answer:
**50 grams of water should be evaporated.**

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