If `a:b=5:7`, then `(5a-3b):(4a-2b)` is equal to :

Options

A. `2:3`
B. `5:4`
C. `4:3`
D. `3:2`

Answer

To solve the problem, we start with the given ratio \( a:b = 5:7 \). We need to find the value of the expression \( (5a - 3b):(4a - 2b) \).

### Step-by-Step Solution:

1. **Express \( a \) and \( b \) in terms of a common variable**:
Since \( a:b = 5:7 \), we can express \( a \) and \( b \) as:
\[ a = 5k \quad \text{and} \quad b = 7k \]
where \( k \) is a positive constant.

2. **Substitute \( a \) and \( b \) into the expression**:
We substitute \( a \) and \( b \) into the expression \( (5a - 3b):(4a - 2b) \):
\[ 5a - 3b = 5(5k) - 3(7k) = 25k - 21k = 4k \]
\[ 4a - 2b = 4(5k) - 2(7k) = 20k - 14k = 6k \]

3. **Form the ratio**:
Now we can form the ratio:
\[ (5a - 3b):(4a - 2b) = 4k:6k \]

4. **Simplify the ratio**:
We can simplify the ratio \( 4k:6k \) by dividing both terms by \( 2k \):
\[ \frac{4k}{2k} : \frac{6k}{2k} = 2:3 \]

5. **Final answer**:
Therefore, the value of \( (5a - 3b):(4a - 2b) \) is:
\[ \boxed{2:3} \]