The age of Jim Hawkins is never specified in the text, but it can be assumed that he is in his early teenage years. After all, Jim is hired on the Hispaniola as a cabin boy, and the average age of cabin boys tended to be between twelve and sixteen years old.

Additionally, Jim's being assigned to put the treasure into bread bags rather than to help carry it to the ship also suggests that Jim is still rather small. Jim himself says,

For my part, as I was not much use at carrying, I was kept busy all day in the cave packing the minted money into bread-bags.

His presumably small size makes it easy to surmise that he is around twelve to fourteen years old. Most illustrations of the novel and movie adaptations present Jim as around thirteen or fourteen years old. Film versions usually cast actors within that age range or slightly older. A few other versions, such as Disney's Treasure Planet, present Jim in his older teens, but the general view seems to put Jim at the younger end of his adolescence, since Treasure Island is just as much a coming-of-age story as it is a swashbuckling adventure.

From what can be observed in the text, Jim is at an age where he is still largely viewed by the adults around him as a child, but he is nevertheless expected and allowed to take on certain adult responsibilities. Over the course of the novel, he comes of age, developing from the frightened young boy of the early chapters into someone mature and discerning enough to respect but not trust Long John Silver. Hence, the age range of twelve to fourteen makes the most sense, judging by the trajectory of Jim's character development and the way the adults react to him.