Explanation:

Let’s break it down:

- You’re given: 9 : 91 :: 13 : ?

- The pattern here isn’t complicated math; it’s simply reversing the digits and sticking them together.

- 9 reversed and then stuck to 1? Actually, no—look closer. 9 ? 91

- 9 × 10 + 1 = 91 (so, number × 10 + 1)

- Let’s apply the same to 13:

- 13 × 10 + 1 = 131

- Wait, but none of the options is 131.

- Maybe the trick is number × itself + itself? Let’s check:

- 9 × 9 + 1 = 82

- Not matching.

- Now, how about the “mirror” format (writing the number backward and then forward)?

- 9 ? 9 and then 1, doesn’t fit.

- Check if it’s 9 written as 91 (reverse digits). For 13, that’s 31.

- That’s not an option.

- Let’s check: 9 : 91 (if you just write 9 first and then 1 after it, 91). Similarly, 13, make it 13 and then 1 ? 131.

- That’s not an option.

- Maybe it's n × (n+1): 9×(9+1)=90, not 91.

- 9 × 10 + 1 = 91 (already checked).

- 13 × 14 = 182 (close to 183).

Look at the options:

- Option 1, 183: 13 × 14 + 1 = 183.

- Option 2, 99 (does not fit).

- Option 3, 132 (does not fit).

- Option 4, 203 (does not fit).

Here’s the thing: For 9, 9 × 10 + 1 = 91

- For 13, 13 × 14 + 1 = 183

- That’s consistent logic.

So, the answer is

Option 1: 183