Identify the likely nature of compound $P$

The reagent $C H_3MgBr$ (excess) in dry ether followed by hydrolysis indicates a Grignard addition to a carbonyl compound.

Since the problem mentions "Et in compound $P$ is ethyl group", the usual intended structure is an aromatic carbonyl compound containing an ethyl substituent on benzene. Grignard reagent adds to the carbonyl carbon, giving an alcohol $Q$.

Nature of $Q \to R$ using $H_2SO_4$ at $0^\circ C$

Concentrated $H_2SO_4$ at low temperature on an alkyl benzene typically causes aromatic sulfonation.

If $Q$ is an alkyl-substituted aromatic alcohol, the ring is activated by alkyl-type substituents, and treatment with cold $H_2SO_4$ gives the corresponding aryl sulfonic acid $R$.

So, $Q \to R$ is aromatic sulfonation.

Nature of $R \to S$ using $CH_3COCl/AlCl_3$ followed by water

The reagent set $CH_3COCl/AlCl_3$ is the standard condition for Friedel–Crafts acylation.

Therefore, $R \to S$ is Friedel–Crafts acylation.

Match with options

• A: Dehydration and Friedel–Crafts acylation
  First step incorrect.
• B: Aromatic sulfonation and Friedel–Crafts acylation
  Matches the reaction types deduced.
• C: Friedel–Crafts alkylation, dehydration and Friedel–Crafts acylation
  Extra step not indicated.
• D: Friedel–Crafts alkylation and Friedel–Crafts acylation
  First step incorrect.

Derived answer

Hence, the reactions $Q \to R$ and $R \to S$ are: $\boxed{\text{Aromatic sulfonation and Friedel–Crafts acylation}}$

So the correct option is B.

Comparison with stored answer

Stored correct answer = D.
My derived answer = B.

These do not match. The step $Q \to R$ with $H_2SO_4$ at $0^\circ C$ is much more consistent with sulfonation, not Friedel–Crafts alkylation.