If `( 3a + 5b)/( 3 a - 5 b) = 5` then a : b is equal to

Options

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

Answer

To solve the equation \(\frac{3a + 5b}{3a - 5b} = 5\) and find the ratio \(a : b\), we can follow these steps:

### Step 1: Cross-multiply the equation
We start with the equation:
\[ \frac{3a + 5b}{3a - 5b} = 5 \]
Cross-multiplying gives us:
\[ 3a + 5b = 5(3a - 5b) \]

### Step 2: Distribute on the right side
Expanding the right side:
\[ 3a + 5b = 15a - 25b \]

### Step 3: Rearrange the equation
Now, we can rearrange the equation to isolate terms involving \(a\) and \(b\):
\[ 3a + 5b - 15a + 25b = 0 \]
This simplifies to:
\[ -12a + 30b = 0 \]

### Step 4: Factor out common terms
We can factor out the common terms:
\[ 12a = 30b \]

### Step 5: Simplify the equation
Dividing both sides by 6 gives:
\[ 2a = 5b \]

### Step 6: Find the ratio \(a : b\)
To express \(a\) in terms of \(b\), we can rearrange the equation:
\[ \frac{a}{b} = \frac{5}{2} \]
Thus, the ratio \(a : b\) is:
\[ a : b = 5 : 2 \]

### Final Answer
The ratio \(a : b\) is \(5 : 2\).

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