I strongly believe that a carbocation should not rearrange to another if there are no **immediate** benefits(like a [Greedy Algorithm](https://en.wikipedia.org/wiki/Greedy_algorithm)).

[![reaction and possible products](https://i.stack.imgur.com/10rjEm.png)](https://i.stack.imgur.com/10rjEm.png)

The doubt hit me while solving this question. The answer mentioned in the book answers (b) but my answer comes out to be (a).

Here is the mechanism:

[![mechanism](https://i.stack.imgur.com/LfodU.png)](https://i.stack.imgur.com/LfodU.png)