Step 1: Understanding the Concept:
This is a problem-based question that requires applying the principles of the Indian Penal Code, 1860, to a factual scenario to identify the correct offence. The key is to analyze the elements of each offence listed in the options.
Step 2: Detailed Explanation:
Let's analyze the scenario and match it with the offences:
\[\begin{array}{rl} \bullet & \text{Theft (Section 378 IPC): Requires dishonest taking of movable property out of the possession of a person without their consent. Here, A finds the purse; it is not in anyone's possession when he finds it. So, there is no 'taking from possession'. Thus, it is not theft. } \\ \bullet & \text{Criminal breach of trust (Section 405 IPC): Requires an entrustment of property. A was never entrusted with the purse by B. He found it by chance. Therefore, it is not a criminal breach of trust. } \\ \bullet & \text{Cheating (Section 415 IPC): Requires deception of a person to fraudulently induce them to deliver property. A did not deceive anyone to get the purse. Thus, it is not cheating. } \\ \bullet & \text{Criminal misappropriation (Section 403 IPC): Occurs when a person dishonestly misappropriates or converts to his own use any movable property. Explanation 2 to Section 403 directly covers this scenario. A finder of lost property who, despite knowing or having the means of discovering the owner, appropriates it for his own use is guilty of this offence. Initially, A's finding was innocent. The crime was committed when he afterwards discovered the owner (B) and then decided to appropriate the money. This perfectly fits the definition of criminal misappropriation. } \\ \end{array}\]
Step 3: Final Answer:
The correct answer is (C) as A's act of appropriating the found property to his own use after discovering its rightful owner constitutes the offence of criminal misappropriation under Section 403 of the IPC.