Step 1: The given reaction starts with an acid chloride reacting in presence of $AlCl_3$.
This indicates a Friedel–Crafts acylation reaction.
Step 2: In presence of $AlCl_3$, acid chloride generates an acylium ion:
\[
RCOCl + AlCl_3 \rightarrow RCO^+ + AlCl_4^-
\]
Step 3: Since the reaction shown in the question leads to a cyclic ketone, the process is an intramolecular Friedel–Crafts acylation.
Intramolecular reactions are favored when 5- or 6-membered rings can form.
Step 4: Thus, the acid chloride cyclizes to form a cyclic ketone as the intermediate product.
Step 5: In the next step, the cyclic ketone is treated with aqueous NaOH and heat.
These are standard conditions for an aldol condensation.
Step 6: The ketone has $\alpha$-hydrogens, so it forms an enolate ion in basic medium:
\[
\text{Ketone} + OH^- \rightarrow \text{Enolate ion}
\]
Step 7: The enolate attacks the carbonyl carbon intramolecularly, forming a $\beta$-hydroxy ketone.
Step 8: On heating, dehydration occurs, producing an $\alpha,\beta$-unsaturated ketone as the final product.
Step 9: From the given solution data, the molar mass of the final product is $158\,\text{g/mol}$ and it contains only one oxygen atom.
Step 10: Mass of oxygen in one mole of product:
\[
=16\,\text{g}
\]
Step 11: Percentage of oxygen:
\[
%O=\frac{16}{158}\times100=10.13%
\]
Hence, the correct answer is (A) 10.13.