Step 1: Know the target.
Benzoic acid is \(C_6H_5COOH\), a single \(-COOH\) group joined to a benzene ring.
Step 2: Pick the right tool.
A strong oxidising agent such as alkaline \(KMnO_4\) followed by acid can shorten any side chain (as long as there is a benzylic hydrogen) down to \(-COOH\).
Step 3: Convert acetophenone (I).
Acetophenone is \(C_6H_5COCH_3\). On vigorous oxidation with alkaline \(KMnO_4\), the methyl-carbonyl side chain is cut and oxidised to give benzoic acid.
\[C_6H_5COCH_3 \xrightarrow{KMnO_4/OH^-, \; then \; H^+} C_6H_5COOH\]
Step 4: Convert ethyl benzene (II).
Ethyl benzene is \(C_6H_5CH_2CH_3\). It has benzylic hydrogens, so hot alkaline \(KMnO_4\) oxidises the whole side chain to a single \(-COOH\).
\[C_6H_5CH_2CH_3 \xrightarrow{KMnO_4/OH^-, \; then \; H^+} C_6H_5COOH\]
Step 5: Note the common point.
In both cases only one carbon stays on the ring as \(-COOH\); the extra carbons are lost as \(CO_2\) and carbonate.
Answer: Both acetophenone and ethyl benzene give benzoic acid on oxidation with hot alkaline \(KMnO_4\) followed by acidification.