Explanation:

- Cyclist 1 travels at 30 km/h and Cyclist 2 at 25 km/h around a 75 km circular track.

- The goal is to find when they both meet at their starting point after setting off.

- For a complete cycle around the track, Cyclist 1 takes \( \frac{75 \text{ km}}{30 \text{ km/h}} = 2.5 \) hours.

- Cyclist 2 takes \( \frac{75 \text{ km}}{25 \text{ km/h}} = 3 \) hours.

- To meet at the starting point again, we need the least common multiple (LCM) of their lap times (2.5 and 3 hours).

- LCM of 2.5 and 3 is 15 hours.

- Thus, they will both be back at the starting point after 15 hours.

- Correct Option: 4, 15 hours