The ratio of acid to water in solutions A and B is 2: 7 and 4: 5, respectively. these solutions are mixed in the ratio of 4:3. What is the ratio of acid to water in the resulting solution?

Options

A. `25 : 21 `
B. `23:40 `
C. `21:40
`
D. `20:43
`

Answer

To solve the problem, we need to find the ratio of acid to water in the resulting solution after mixing solutions A and B in the given ratio. Let's break it down step by step:

### Step 1: Determine the components of Solution A
The ratio of acid to water in Solution A is 2:7. This means that for every 2 parts of acid, there are 7 parts of water.

- Total parts in Solution A = 2 (acid) + 7 (water) = 9 parts
- Acid in Solution A = \( \frac{2}{9} \)
- Water in Solution A = \( \frac{7}{9} \)

### Step 2: Determine the components of Solution B
The ratio of acid to water in Solution B is 4:5. This means that for every 4 parts of acid, there are 5 parts of water.

- Total parts in Solution B = 4 (acid) + 5 (water) = 9 parts
- Acid in Solution B = \( \frac{4}{9} \)
- Water in Solution B = \( \frac{5}{9} \)

### Step 3: Mix the solutions in the given ratio
We are mixing solutions A and B in the ratio of 4:3.

Let’s assume we take 4 parts of Solution A and 3 parts of Solution B.

### Step 4: Calculate the total acid and water from both solutions
**From Solution A (4 parts):**
- Acid from A = \( 4 \times \frac{2}{9} = \frac{8}{9} \)
- Water from A = \( 4 \times \frac{7}{9} = \frac{28}{9} \)

**From Solution B (3 parts):**
- Acid from B = \( 3 \times \frac{4}{9} = \frac{12}{9} \)
- Water from B = \( 3 \times \frac{5}{9} = \frac{15}{9} \)

### Step 5: Add the acid and water from both solutions
**Total Acid:**
\[ \text{Total Acid} = \frac{8}{9} + \frac{12}{9} = \frac{20}{9} \]

**Total Water:**
\[ \text{Total Water} = \frac{28}{9} + \frac{15}{9} = \frac{43}{9} \]

### Step 6: Find the ratio of acid to water in the resulting solution
The ratio of acid to water is given by:
\[ \text{Ratio of Acid to Water} = \frac{\text{Total Acid}}{\text{Total Water}} = \frac{\frac{20}{9}}{\frac{43}{9}} = \frac{20}{43} \]

Thus, the ratio of acid to water in the resulting solution is \( 20:43 \).

### Final Answer
The ratio of acid to water in the resulting solution is \( 20:43 \).

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