Step 1: Doctrine of part performance.
The doctrine of part performance under Section 53A of the Transfer of Property Act protects a transferee who has acted on a contract relating to immovable property.
Step 2: Essential requirement.
A mandatory condition for invoking Section 53A is that the transferee must prove that he has performed or is willing to perform his part of the contract.
Step 3: Evaluation of options.
Mere continuation of possession is insufficient. Lack of willingness defeats the claim. Readiness and willingness are indispensable.
Step 4: Conclusion.
Hence, option (C) correctly states the law.