If x: y = 5:7 , then (6x-y) : (5x+ 3y) is equal to :

Options

A. `1:4`
B. `11:2`
C. `4:1`
D. `1:2`

Answer

To solve the problem, we start with the given ratio \( x : y = 5 : 7 \). We can express \( x \) and \( y \) in terms of a common variable \( a \).

### Step 1: Express \( x \) and \( y \) in terms of \( a \)
Let:
\[ x = 5a \quad \text{and} \quad y = 7a \]

### Step 2: Substitute \( x \) and \( y \) into the expression \( 6x - y \) and \( 5x + 3y \)
Now, we need to calculate \( 6x - y \) and \( 5x + 3y \):
\[ 6x - y = 6(5a) - 7a = 30a - 7a = 23a \]
\[ 5x + 3y = 5(5a) + 3(7a) = 25a + 21a = 46a \]

### Step 3: Form the ratio \( (6x - y) : (5x + 3y) \)
Now we can form the ratio:
\[ (6x - y) : (5x + 3y) = 23a : 46a \]

### Step 4: Simplify the ratio
The \( a \) in both terms cancels out:
\[ 23a : 46a = 23 : 46 \]
Now, simplify \( 23 : 46 \):
\[ 23 : 46 = 1 : 2 \]

### Final Answer
Thus, the ratio \( (6x - y) : (5x + 3y) \) is equal to:
\[ \boxed{1 : 2} \]