New Zealand Law
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If this is a private sale the Consumer Guarantees Act does not apply. So if you made full disclosure of the defects, then if he used the bike in that knowledge, and further, used it knowing a new issue was present, which needed attention, then he has little chance of claiming against you. So you have made a modest offer to settle which in my view more than satisfies your legal obligations. Getting someone to mediate the dispute is a good idea, but I consider you are in a strong position.