If `P : Q = 9 : 7`, then what is the value of `(P - Q) : (P + Q)`?

Options

A. `1:2`
B. `1:8`
C. `1:4`
D. `2:13`

Answer

To solve the problem, we need to find the value of \((P - Q) : (P + Q)\) given that \(P : Q = 9 : 7\).

### Step-by-Step Solution:

1. **Express P and Q in terms of a common variable (k)**:
Since \(P : Q = 9 : 7\), we can express \(P\) and \(Q\) as:
\[ P = 9k \quad \text{and} \quad Q = 7k \]

2. **Calculate \(P - Q\)**:
Now, we can find \(P - Q\):
\[ P - Q = 9k - 7k = 2k \]

3. **Calculate \(P + Q\)**:
Next, we find \(P + Q\):
\[ P + Q = 9k + 7k = 16k \]

4. **Form the ratio \((P - Q) : (P + Q)\)**:
Now we can write the ratio:
\[ (P - Q) : (P + Q) = 2k : 16k \]

5. **Simplify the ratio**:
We can simplify the ratio by canceling \(k\) from both terms:
\[ 2k : 16k = 2 : 16 \]
Further simplifying gives:
\[ 2 : 16 = 1 : 8 \]

### Final Answer:
Thus, the value of \((P - Q) : (P + Q)\) is:
\[ \boxed{1 : 8} \]