`(17 : 8)` as `(25 : 7) :: (32:5)` as `(overset(?)(-) : overset(?)(-))`

Options

A. `39:12`
B. `27:9`
C. `37:10`
D. `29:11`

Answer

To solve the problem `(17 : 8) as (25 : 7) :: (32 : 5) as (overset(?)(-) : overset(?)(-))`, we need to find the values that correspond to the question marks in the ratio.

### Step-by-Step Solution:

1. **Understanding the Ratios**:
We have the ratios:
- \( 17 : 8 \) corresponds to \( 25 : 7 \).
- We need to find the corresponding values for \( 32 : 5 \).

2. **Finding the Relationship**:
From the first pair \( (17 : 8) \) and \( (25 : 7) \):
- We can observe that \( 17 + 8 = 25 \).
- We also see that \( 2 + 5 = 7 \) (the sum of the digits of 25).

3. **Applying the Same Logic**:
Now, applying the same logic to the second pair \( (32 : 5) \):
- Calculate \( 32 + 5 \):
\[ 32 + 5 = 37 \]
- Now, we need to find the sum of the digits of 37:
\[ 3 + 7 = 10 \]

4. **Forming the Final Ratio**:
Thus, the corresponding values for \( (32 : 5) \) will be \( 37 : 10 \).

5. **Final Answer**:
Therefore, the answer to the question is:
\[ (32 : 5) \text{ corresponds to } (37 : 10) \]