Step 1: Identify the first reaction with \( \text{Zn}/\text{Hg} / \text{Conc. HCl} \).
The reaction with \( \text{Zn}/\text{Hg} \) in the presence of concentrated HCl is a classic Clemmensen reduction, which reduces the aldehyde group (\( \text{-CHO} \)) to a methyl group (\( \text{-CH}_3 \)). The starting material is \( \text{p-methylbenzaldehyde} \), which is reduced to \( \text{p-xylene} \) (1,4-dimethylbenzene).
\[
\text{p-methylbenzaldehyde} \xrightarrow{\text{Zn}/\text{Hg}, \text{Conc. HCl}} \text{p-xylene}
\]
Step 2: Analyze the reaction with Tollen's reagent.
Tollen's reagent is used to detect aldehydes. It reduces the aldehyde group in \( \text{p-methylbenzaldehyde} \), confirming the presence of the aldehyde functional group.
Step 3: Oxidation with \( \text{KMnO}_4 / H^+ \).
On oxidation with \( \text{KMnO}_4 / H^+ \), the methyl group in \( \text{p-xylene} \) is oxidized to a carboxyl group, resulting in the formation of 1,4-benzenedicarboxylic acid, confirming the structure of \( \text{p-methylbenzaldehyde} \).
Step 4: Conclusion.
Based on the reactions described, compound A is \( \text{p-methylbenzaldehyde} \), which reacts as described to yield the correct product. Therefore, the correct answer is option (A).