Explanation:

- The person covers equal distances at three different speeds: 5 km/h, 8 km/h, and 10 km/h.

- Let's assume the distance covered at each speed is 'd' km.

- The time taken to cover distance 'd' at 5 km/h is $\frac{d}{5}$ hours.

- The time taken at 8 km/h is $\frac{d}{8}$ hours.

- The time taken at 10 km/h is $\frac{d}{10}$ hours.

- The total time for all three distances is $\frac{d}{5}+\frac{d}{8}+\frac{d}{10}=2\text{ hours and }33\text{ minutes}$ or $\frac{153}{60}=\frac{51}{20}$ hours.

- Solving $\frac{d}{5}+\frac{d}{8}+\frac{d}{10}=\frac{51}{20}$ gives $\frac{49d}{40}=\frac{51}{20}$.

- Solving for d, we find $d=6$.

- The total distance is $3d=18\text{ km}$.

So, the correct answer is:

Option 1: 18 km

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