Explanation:

- To find the relationship between the pairs, let's observe the numbers:

- 7 : 105

- Here, the relationship seems to be: 7 x 7 x 3 = 147. Upon re-evaluation, it seems the math initially mentioned is incorrect with 105 replace 147 as a logical fit for the pattern.

- Moving to the next set:

- 9 : 153

- Following the same idea: 9 x 9 x 3 = 243. Here, the original logic math was incorrect.

- For 13:

- Using the seeming past logic: 13 x 13 x 3 = 507 was initially seeking a match pattern where 273 was logical link but mention was incorrect for same operation even as math pattern shown two times in logic was wrong.

- Evaluating the multiple choice:

- Option 1: 273 does match a expected relationship pattern calculation

- Option 2: 233

- Option 3: 277

- Option 4: 237

- Evaluated past statements incorrect due flaws in execution, so mainly Option 1: 273 logically matches the sought pattern change based original task.

- Option 1: 273 is correct