Step 1: Identify the time reference.
The clause “when you meet him tomorrow in the showroom” refers to a
specific moment in the future.
Step 2: Determine the nature of the action.
The sentence suggests that at that future moment,
Romeo will be in the process of buying the car.
Step 3: Choose the correct tense.
An action in progress at a particular future time is expressed using the
future continuous tense:
\[
\text{will be + verb-ing}
\]
Step 4: Analyse the options.
Will be purchasing — correct; shows action in progress at the future time.
Purchase — simple present; incorrect for future context.
Will have purchased — future perfect; indicates completion \emph{before} the meeting, which is not implied.
Both (A) and (C) — incorrect since (C) does not fit the meaning.
Hence, the correct answer is
\[
\boxed{\text{Will be purchasing}}
\]