Solution:

"Bodo weighs 110 pounds" is the correct answer. His sister weighs 10 pounds. Thus, Bodo weighs 100 pounds more than his sister and their combined weight is 120 as per the problem requirements.

The common mistake is to quickly jump to the conclusion that "Bodo weighs 100 pounds and his sister weighs 20 pounds." But, Bodo would then erroneously weigh 80 pounds more than his sister.

Alternative Solution through Equations:

Let b be Bodo's weight and s be his sister's weight. Then,

b − s = 100; and
b + s = 120.

On solving the above two equations, we get

b = (100 + 120) / 2 = 110.