2. (10 points) The sum of three natural numbers $A$, $B$, and $C$ is 111. It is known that the average of $A$ and $B$ is 31, and the average of $A$ and $C$ is 37. What is the average of $B$ and $C$ ( )
A. 34
B. 37
C. 43
D. 68
【Analysis】Since the sum of three natural numbers $A, B, C$ is 111, and the average of $A, B$ is 31, the sum of $A, B$ is $31 \times 2=62$. Therefore, $C=111-62=49$. Also, since the average of $A, C$ is 37, $B=111-37 \times 2=37$. Then, using the method of finding the average, we can find the average of $B, C$.

【Solution】Solution: $C=111-31 \times 2=49$,
$$
\begin{aligned}
B= & 111-37 \times 2=37, \\
& (49+37) \div 2, \\
= & 86 \div 2, \\
= & 43
\end{aligned}
$$

Answer: The average of $B, C$ is 43.
Therefore, the correct choice is: $C$.