Calculate the percentage composition of a solution obtained by mixing 200 g of a `30%` and 300 g of a `20%` solution by weight.

Options

A. `50%`
B. `28%`
C. `64%`
D. `24%`

Explanation

To calculate the percentage composition of the solution obtained by mixing 200 g of a 30% solution and 300 g of a 20% solution, follow these steps:

### Step 1: Calculate the amount of solute in the 30% solution
- The formula to calculate the mass of solute is:
\[ \text{Mass of solute} = \text{Weight of solution} \times \left(\frac{\text{Percentage}}{100}\right) \]
- For the 30% solution:
\[ \text{Mass of solute} = 200 \, \text{g} \times \left(\frac{30}{100}\right) = 200 \times 0.30 = 60 \, \text{g} \]

### Step 2: Calculate the amount of solute in the 20% solution
- For the 20% solution:
\[ \text{Mass of solute} = 300 \, \text{g} \times \left(\frac{20}{100}\right) = 300 \times 0.20 = 60 \, \text{g} \]

### Step 3: Calculate the total mass of solute in the mixed solution
- Total mass of solute:
\[ \text{Total mass of solute} = 60 \, \text{g} + 60 \, \text{g} = 120 \, \text{g} \]

### Step 4: Calculate the total mass of the mixed solution
- Total mass of the solution:
\[ \text{Total mass of solution} = 200 \, \text{g} + 300 \, \text{g} = 500 \, \text{g} \]

### Step 5: Calculate the percentage composition of the final solution
- The formula for percentage composition is:
\[ \text{Percentage composition} = \left(\frac{\text{Mass of solute}}{\text{Total mass of solution}}\right) \times 100 \]
- Substituting the values:
\[ \text{Percentage composition} = \left(\frac{120 \, \text{g}}{500 \, \text{g}}\right) \times 100 = 0.24 \times 100 = 24\% \]

### Final Answer
The percentage composition of the final solution is **24%**.

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