Explanation:

- There are initially nine people with an average weight of 25 kg.

- The total weight of these nine people is $9\times 25=225$ kg.

- A new person joins, and the average weight becomes 26 kg for ten people.

- The total weight for 10 people is $10\times 26=260$ kg.

- The weight of the new person is the difference in total weight before and after: $260-225=35$ kg.

- Option 1: 35 kg is the correct weight of the new person.

Answer: Option 1 - 35 kg