If `(3a + 5b) : (3a - 5b)` = `5 : 1` then `a : b` = ?

Options

A. `2 : 1`
B. `3 : 2`
C. `2 : 5`
D. `5 : 3`

Answer

To solve the problem `(3a + 5b) : (3a - 5b) = 5 : 1`, we will follow these steps:

### Step-by-Step Solution:

1. **Set up the equation using the ratio**:
\[ \frac{3a + 5b}{3a - 5b} = \frac{5}{1} \]

2. **Cross multiply to eliminate the fraction**:
\[ 3a + 5b = 5(3a - 5b) \]

3. **Expand the right side**:
\[ 3a + 5b = 15a - 25b \]

4. **Rearrange the equation to isolate terms involving 'a' and 'b'**:
\[ 3a + 5b + 25b = 15a \]
\[ 3a + 30b = 15a \]

5. **Move all terms involving 'a' to one side and 'b' to the other side**:
\[ 30b = 15a - 3a \]
\[ 30b = 12a \]

6. **Divide both sides by 12 to express 'a' in terms of 'b'**:
\[ \frac{a}{b} = \frac{30}{12} \]

7. **Simplify the fraction**:
\[ \frac{a}{b} = \frac{5}{2} \]

8. **Write the final ratio**:
\[ a : b = 5 : 2 \]

### Final Answer:
\[ a : b = 5 : 2 \]