Step 1: Understand the Kjeldahl back-titration.
Nitrogen in the sample turns into ammonia, which is absorbed by a known excess of HCl. The unreacted HCl is then titrated with NaOH, so the difference tells us how much HCl the ammonia used.
Step 2: Find total milliequivalents of HCl.
Total HCl $= 30 \text{ mL} \times 1 \text{ N} = 30$ meq.
Step 3: Find HCl left over.
The back-titrating NaOH is $120 \text{ mL} \times 0.1 \text{ N} = 12$ meq, which equals the leftover HCl.
Step 4: Find HCl used by ammonia.
HCl that reacted with ammonia $= 30 - 12 = 18$ meq, and this equals the meq of nitrogen.
Step 5: Convert to mass of nitrogen.
Mass of N $= \dfrac{18 \times 14}{1000} = 0.252$ g.
Step 6: Find the percentage.
\[ \% N = \frac{0.252}{1.5} \times 100 \approx 18.6\% \] which is option 1.
\[ \boxed{18.6} \]