Answer: C — 13.85 s (approx)

Find the length of the train using the same-direction crossing.

Relative speed when $P$ moves in the same direction as $T$: $v_{\text{same}} = 100 - 4 = 96 \text{ km/h} = \frac{96{}000}{3600} = \frac{80}{3} \text{ m/s}$

Length of train $L = v_{\text{same}} \times 15 = \frac{80}{3} \times 15 = 400$ m.

Time to cross when moving in opposite directions.

Relative speed: $v_{\text{opp}} = 100 + 4 = 104 \text{ km/h} = \frac{104{}000}{3600} = \frac{260}{9} \text{ m/s}$

Time to cross: $t = \frac{L}{v_{\text{opp}}} = \frac{400}{260/9} = \frac{400 \times 9}{260} = \frac{3600}{260} \approx 13.846 \text{ s}$

So $t \approx 13.85$ s.