Mr. A and Mr. B both believed a specific bicycle existed and was being sold, but unknown to either of them, it had already been destroyed by fire before they entered the agreement.
Checking against the requirements for a void agreement, both parties were mistaken (neither knew of the fire), the mistake was one of fact (the physical existence of the bicycle), and that fact was essential to the agreement (you cannot sell an object that no longer exists). All three conditions line up together.
The suggestion that this is a mistake of law does not fit, since nothing about legal rules is in question here, only an unknown physical event. Equally, the idea that only one party was mistaken is wrong, since both were equally unaware, and the question of whether the promise was performed has no bearing on a defect that existed right from the moment of agreement.
So the agreement is void, since it rests on a mutual mistake about a fact, the bicycle's existence, that was essential to the bargain.
Ms. X and Ms. Y both wrongly believed that the law in force in India permitted the sale of the article. The key here is identifying what kind of mistake this is, a mistake about a physical or factual detail, or a mistake about what the law says.
Believing that something is legally permitted when it is not is a mistake about a rule of law, not about a fact. The doctrine that renders agreements void only reaches mistakes of fact shared by both parties, it deliberately excludes mistakes of law.
Since the mistake here is one of law and is shared equally by both Ms. X and Ms. Y, neither of them individually gets a right to avoid the contract, and the contract as a whole does not become voidable either. Options that grant Ms. X or Ms. Y a personal option to avoid, or that call the contract simply valid without reasoning, both miss this point.
So the contract is not voidable, because a shared mistake of law carries no legal consequence of this kind.
Mr. J and Mr. K used the same word, "club", to mean two completely different things, a golf club for Mr. J and a clubhouse for Mr. K. This is a classic case of latent ambiguity in the subject-matter of a contract.
Because each party had an entirely different object in mind, there was never a true meeting of the minds on what was actually being sold, so, in one sense, the mistake defeated real consent from forming at all. At the same time, each party proceeded believing they were buying or selling a specific, identifiable thing, so the mistake also misled them as to the very purpose of the bargain they thought they were making.
This is not a case about the identity of the parties, both knew exactly who they were dealing with, the confusion is purely about the subject-matter itself. Since both effects, the failure of real consent and the misleading of the parties as to purpose, are present together and are not contradictory, the fuller and more accurate explanation covers both.
So the agreement is void because both (A) and (B) correctly capture what went wrong.
Mr. D intended to grant a lease, and Mr. K agreed to manage the cultivation on the strength of getting that lease, but the deed they actually signed turned out to be a gift deed, and neither of them realised this at the time.
Whether a document is a lease or a gift is a question of fact about what that document actually is and does, not a question of legal rules, so this rules out any option framing it as a mistake of law.
The mistake was also not confined to Mr. D alone. Mr. K equally believed he was receiving a leasehold interest in return for his management services, so he shared the same false understanding about the deed's true character. Since the nature of the document goes to the very core of the bargain between them, essential and shared by both, this is a mutual mistake of fact.
So Mr. D and Mr. K were both mistaken about a fact essential to their agreement.
Here, delivery of the article was completed on the date both parties agreed to, even though it travelled on a different ship than originally named. The name of the ship was never a term the parties treated as central to their bargain, so mixing it up does not strike at the root of the contract.
The agreement stands, so the correct answer is the agreement is valid as both parties were under a mistake as to a matter of fact not essential to the agreement.