Step 1: Acid initially = 20 mL of 0.1 M
\[
\text{milli-mole HCl} = 20 \times 0.1 = 2.
\]
Step 2: Back-titrated by 15 mL NaOH
\[
= 15 \times 0.1 = 1.5 \text{ milli-mole}.
\]
Step 3: Acid reacted with NH$_3$
\[
= 2 - 1.5 = 0.5 \text{ milli-mole}.
\]
Step 4: In Kjeldahl
1 mole N → 1 mole NH$_3$ neutralizes 1 mole HCl.
Therefore
\[
\text{mole of N in sample} = 0.5 \times 10^{-3}.
\]
Step 5: Mass of N
\[
= 14 \times 0.5 \times 10^{-3} = 7 \times 10^{-3} \text{ g}.
\]
Step 6: Sample mass
29.5 mg = 0.0295 g.
\[
%\;N = \frac{0.007}{0.0295} \times 100 = 23.7%.
\]
Hence → (C).