A solution of 100L contains 75 percent water and rest liquid sugar. How much liquid sugar must be added to make 50 percent sugar solution?

Options

A. 30 L
B. 20 L
C. 25 L
D. 50 L

Answer

To solve the problem step by step, we need to determine how much liquid sugar must be added to a 100L solution that contains 75% water and 25% liquid sugar in order to create a 50% sugar solution.

### Step-by-Step Solution:

1. **Identify the Initial Composition of the Solution:**
- The total volume of the solution is 100L.
- The solution contains 75% water and 25% liquid sugar.
- Therefore, the amount of water in the solution is:
\[ \text{Water} = 75\% \text{ of } 100L = 75L \]
- The amount of liquid sugar in the solution is:
\[ \text{Sugar} = 25\% \text{ of } 100L = 25L \]

2. **Let x be the amount of liquid sugar to be added:**
- After adding x liters of liquid sugar, the new amount of sugar will be:
\[ \text{New Sugar Amount} = 25L + x \]
- The total volume of the solution after adding x liters of sugar will be:
\[ \text{New Total Volume} = 100L + x \]

3. **Set up the equation for the desired concentration:**
- We want the final solution to be a 50% sugar solution. Therefore, we can set up the equation:
\[ \frac{25 + x}{100 + x} = 0.5 \]

4. **Cross-multiply to solve for x:**
- Cross-multiplying gives:
\[ 25 + x = 0.5(100 + x) \]
- Expanding the right side:
\[ 25 + x = 50 + 0.5x \]

5. **Rearranging the equation:**
- Move all terms involving x to one side and constant terms to the other:
\[ 25 + x - 0.5x = 50 \]
\[ 0.5x = 50 - 25 \]
\[ 0.5x = 25 \]

6. **Solving for x:**
- Multiply both sides by 2 to isolate x:
\[ x = 25 \times 2 = 50L \]

7. **Conclusion:**
- Therefore, the amount of liquid sugar that must be added to make a 50% sugar solution is:
\[ \text{Liquid Sugar to be added} = 50L \]

### Final Answer:
50 liters of liquid sugar must be added.