In the questions, there is a certain relationship between the two given numbers on one side of :: and one number is given on another side of :: . It is required to find another number from the given alternative having the same relationship with this number as the numbers of the given pair has :
16:56:: 32:?

Options

A. 96
B. 112
C. 118
D. 128

Explanation

To solve the analogy problem 16:56::32:?, we need to identify the relationship between the first pair of numbers (16 and 56) and apply the same relationship to the second number (32) to find the missing number.

### Step-by-Step Solution:

1. **Identify the relationship between 16 and 56:**
- We start with the first number, 16.
- To find out how we get from 16 to 56, we can try multiplication.
- If we multiply 16 by 3, we get:
\[ 16 \times 3 = 48 \]
- Now, we need to get from 48 to 56. We can see that:
\[ 56 - 48 = 8 \]
- Notice that 8 is half of 16 (i.e., \( \frac{16}{2} = 8 \)).
- Therefore, the relationship can be expressed as:
\[ 56 = (16 \times 3) + \left(\frac{16}{2}\right) \]

2. **Apply the same relationship to 32:**
- Now, we take the second number, which is 32.
- We will multiply 32 by 3:
\[ 32 \times 3 = 96 \]
- Next, we need to add half of 32 to 96:
\[ \frac{32}{2} = 16 \]
- Now, we add this to 96:
\[ 96 + 16 = 112 \]

3. **Conclusion:**
- The missing number that corresponds to 32 in the analogy is 112.

### Final Answer:
The answer is 112.