Select the related number from the given alternatives
`5: 27: : 9` : ?

Options

A. 91
B. 86
C. 83
D. 78

Answer

To solve the problem, we need to identify the relationship between the numbers given in the first pair (5 and 27) and then apply the same relationship to the second number (9) to find the unknown value.

### Step-by-Step Solution:

1. **Identify the relationship between 5 and 27:**
- First, we calculate the square of 5.
- \( 5^2 = 25 \)
- Next, we see how we can get from 25 to 27.
- \( 25 + 2 = 27 \)
- So, the relationship can be expressed as:
\[ 5^2 + 2 = 27 \]

2. **Apply the same relationship to 9:**
- Now, we need to find the value related to 9 using the same pattern.
- First, calculate the square of 9.
- \( 9^2 = 81 \)
- Now, we add 2 to this result:
- \( 81 + 2 = 83 \)
- Therefore, we can express this as:
\[ 9^2 + 2 = 83 \]

3. **Conclusion:**
- The number that relates to 9 in the same way that 27 relates to 5 is 83.

Thus, the answer is **83**.