(a) That's wrong. Late performance is certainly a breach of contract. But is it a breach of sufficient seriousness to justify putting an end to further performance? The question here is whether timely performance is of fundamental importance to the contract or not.
The common law took a strict approach to such questions, treating late performance as a breach of condition. But legislation has been enacted requiring the courts to adopt an equitable approach. Accordingly, promises in a contract should be treated as non-essential terms unless the facts show that the parties intended otherwise. If, in the circumstances of the case, the time of performance is not intended to be important (or 'of the essence'), late performance does not justify terminating further performance: it only allows a claim for damages.
In the present case, there are no facts that suggest payment of the price on the 30th was fundamental to the contract. A is therefore not entitled to terminate performance of the sale.