100gm of an aq. solution of sugar contains 30% sugar by mass. How much water should be evaporated get 40% sugar solution by mass?

Explanation

To solve the problem, we need to determine how much water should be evaporated from a 100 g sugar solution that initially contains 30% sugar by mass, in order to achieve a final solution that is 40% sugar by mass.

### Step-by-Step Solution:

1. **Determine the initial mass of sugar and water:**
- The total mass of the solution is given as 100 g.
- The mass of sugar in the solution is 30% of 100 g:
\[ \text{Mass of sugar} = 30\% \times 100 \, \text{g} = 30 \, \text{g} \]
- The mass of water in the solution is the remaining mass:
\[ \text{Mass of water} = 100 \, \text{g} - 30 \, \text{g} = 70 \, \text{g} \]

2. **Set up the final condition for the solution:**
- We want the final solution to be 40% sugar by mass.
- Let \( x \) be the mass of water that needs to be evaporated.
- After evaporation, the mass of the solution will be:
\[ \text{Final mass of solution} = (70 \, \text{g} - x) + 30 \, \text{g} = 100 \, \text{g} - x \]

3. **Set up the equation for the final concentration:**
- The final concentration of sugar should be 40%, which means:
\[ \frac{\text{Mass of sugar}}{\text{Final mass of solution}} = 40\% \]
- Substituting the known values:
\[ \frac{30 \, \text{g}}{100 \, \text{g} - x} = 0.40 \]

4. **Solve the equation for \( x \):**
- Cross-multiply to eliminate the fraction:
\[ 30 = 0.40 \times (100 - x) \]
- Distributing the 0.40:
\[ 30 = 40 - 0.40x \]
- Rearranging the equation:
\[ 0.40x = 40 - 30 \]
\[ 0.40x = 10 \]
- Solving for \( x \):
\[ x = \frac{10}{0.40} = 25 \, \text{g} \]

5. **Conclusion:**
- The amount of water that should be evaporated to obtain a 40% sugar solution is **25 g**.