One type of liquid contains 20% water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The water in the new mixture in the glass is

Options

A. 0.37
B. 0.46
C. 12 `1/7` %
D. 24 `2/7` %

Answer

To solve the problem step by step, we will use the concept of alligation to find the percentage of water in the mixture of the two liquids.

### Step-by-Step Solution:

1. **Identify the Components**:
- Liquid A (first liquid) contains 20% water.
- Liquid B (second liquid) contains 35% water.

2. **Determine the Parts of Each Liquid**:
- We are mixing 10 parts of Liquid A and 4 parts of Liquid B.

3. **Set Up the Alligation Formula**:
- Let \( x \) be the percentage of water in the mixture.
- According to the alligation rule:
\[ \frac{35 - x}{x - 20} = \frac{10}{4} \]

4. **Cross Multiply**:
- Cross multiplying gives:
\[ 4(35 - x) = 10(x - 20) \]

5. **Expand Both Sides**:
- Expanding the equation:
\[ 140 - 4x = 10x - 200 \]

6. **Rearrange the Equation**:
- Bring all terms involving \( x \) to one side:
\[ 140 + 200 = 10x + 4x \]
\[ 340 = 14x \]

7. **Solve for \( x \)**:
- Divide both sides by 14:
\[ x = \frac{340}{14} \]
- Simplifying \( \frac{340}{14} \):
\[ x = 24.2857 \text{ (approximately)} \]

8. **Convert to Percentage**:
- The percentage of water in the mixture is approximately \( 24.29\% \).

### Final Answer:
The percentage of water in the new mixture in the glass is approximately **24.29%**.