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).
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The conflict between Ralph and Jack is directly an example of Reason Vs. Savagery or Superego (knowledgeable) Ralph Vs. Id (apart of your mind that is selfish and wants everything now) Jack.
I've never thought about that... that was a great book, but i guess the world will never know if the coflict was ever solved...
When both Jack and Ralph stood as possible leaders Roger suggested that they should have a vote. The result was that Ralph was elected as leader and placed Jack in charge of the former choir as a consolation prize.
Ralph and Jack never liked each other. Once they met and Jack wanted to take the power from Ralph there was instant friction between the two. It's was obviously Ralph's job to be chief and Jack just expected to get it instead of Ralph.
There was no real conflict in chapter one; The Sound of the Shell. Ralph and Jack were both contenders to be chief but the issue was settle by a vote, which Ralph won. The only other slight conflict was when Ralph chose Jack and Simon to accompany him on the expedition to climb the mountain. Piggy wanted to go to and Jack told him in no uncertain terms that he wasn't wanted.