Explanation:

- The initial average weight of the team was calculated as 59.8 kg.

- The sum of all members' weights for 20 people is \(59.8 \times 20 = 1196\) kg.

- A weight was misread as 68 kg; it should have been 77 kg.

- The actual sum should be \(1196 - 68 + 77 = 1205\) kg.

- The correct average is \(1205 \div 20 = 60.25\) kg.

So, the correct option is:

- Option 3: 60.25 kg