Correct Answer: nook and corner

Solution : The correct option is the third option.

Explanation:
This idiom means that the news spread everywhere in the city, reaching even the smallest or most remote places. It refers to every small or hidden place, leaving no part of the city untouched by the news.

The meanings of the other options are as follows:
Rack and ruin: This phrase means a state of destruction or decay.
Ins and outs: This phrase refers to the details or intricacies of a subject.
Life and soul: This phrase refers to the most lively or energetic person in a group or the heart of a party.

Therefore, the complete sentence should be: The news of his arrest spread rapidly in every nook and corner of the city.