At the time Ralph thought that he was offering Jack the consolation of being put in charge of the former choir, which Jack then decided would become hunters. Later with the perspective of hindsight Ralph may well have regretted that decision.
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When Ralph is elected to be chief he knows Jack is dissapointed (as Jack also wished to be chief) so he appoints Jack as leader of the choir and asks him what he wants them to be, to which Jack replies, "hunters."
Jack accused Ralph of not being fit to be a leader. He then asked the boys if they should fire Ralph as chief, but no one responds. Jack runs off crying and says that he is not going to be a part of Ralph's group anymore
There is always an underlying conflict between Ralph and Jack, primarily on Jack's part. Jack has always been use to being in command of his choir and resents the fact that a group of children for whom he holds no regard or respect elected Ralph into a position of power which he coveted. Later as Ralph, aided only by Simon, attempts to build a third shelter for the use of all the boys he shows his own resentment towards Jack when he says... "They work for five minutes and then wander off or go hunting." Implying that while Jack his having fun hunting he is stuck doing routine and thankless but necessary tasks. The division becomes even wider after the signal fire is allowed to go out and Ralph begins to accept that Jack not only wants his position as chief but that Jack actually hates him too.
If you're talking about the conflict in the beginning of the book concerning who gets to be leader, it was resolved when Ralph allowed Jack to be the leader of the hunters. If you're talking the conflict between the two characters of Jack being savage and Ralph trying to stay civilized, it is never resolved but it is ended when SPOILER ALERT the ship comes and rescues them. You are probably wanting the answer for the conflict in leadership (the first one).
Jack accuses Ralph of not being fit to be the leader and asks the boys if they want Jack fired as chief, but no one responds to him. He runs off crying and saying that he is no longer going to be part of Ralph's group.