If x : y = 7 :5 , then what is the value of `(5X -2y) : (5X + 2y)`

Options

A. `5/4`
B. `6/5`
C. `25 / 31`
D. `31 /42`

Answer

To solve the problem where \( x : y = 7 : 5 \), we need to find the value of \( (5x - 2y) : (5x + 2y) \).

### Step-by-Step Solution:

1. **Express x in terms of y**:
Since \( x : y = 7 : 5 \), we can write:
\[ x = \frac{7}{5}y \]

2. **Substitute x in the expression**:
We need to evaluate \( (5x - 2y) : (5x + 2y) \). Substitute \( x = \frac{7}{5}y \) into the expression:
\[ 5x = 5 \left(\frac{7}{5}y\right) = 7y \]
Now substitute this into the expression:
\[ (5x - 2y) = (7y - 2y) = 5y \]
\[ (5x + 2y) = (7y + 2y) = 9y \]

3. **Form the ratio**:
Now we can form the ratio:
\[ (5x - 2y) : (5x + 2y) = 5y : 9y \]

4. **Simplify the ratio**:
Since \( y \) is common in both terms, we can cancel it out:
\[ 5y : 9y = 5 : 9 \]

### Final Answer:
Thus, the value of \( (5x - 2y) : (5x + 2y) \) is \( 5 : 9 \).