Step 1: Understanding the Concept:
The question presents a factual scenario and asks to identify the corresponding landmark case. The legal principle at the heart of this scenario is a fundamental rule of contract law: for an offer to be validly accepted, the acceptor must have knowledge of the offer. Acceptance in ignorance of the offer is no acceptance at all.
Step 2: Detailed Explanation:
The facts described in the question are the exact facts of the seminal Indian case on contract law, Lalman Shukla v. Gauri Dutt (1913) 11 ALJ 489.
\begin{itemize}
\item In this case, Gauri Dutt's (the defendant) nephew absconded. He sent his servant, Lalman Shukla (the plaintiff), to search for the boy.
\item After the servant had left, Gauri Dutt announced a reward for anyone who found the boy.
\item Lalman Shukla found the boy and brought him back. He was unaware of the reward at the time he found the boy.
\item Later, upon learning of the reward, he sued to claim it.
\item The Allahabad High Court held that Lalman Shukla was not entitled to the reward because he had no knowledge of the offer when he performed the act of finding the boy. To create a valid contract, there must be an acceptance of an offer, and there can be no acceptance without knowledge of the offer.
\end{itemize}
The other cases are irrelevant:
\begin{itemize}
\item Donoghue v. Stevenson: Landmark case on the law of negligence.
\item Tweedle v. Atkinson and Dutton v. Poole: Landmark cases on the doctrine of privity of contract.
\end{itemize}
Step 3: Final Answer:
The case based on these facts is Lalman Shukla v. Gauri Dutt.