Chapter Length

We can first notice that the sum of digits of two consecutive numbers can be even if and only if the first number end with a $9$ (otherwise both numbers will be written as $\overline{a_{n}a_{n-1}...a_{1}a_{0}}$ and $\overline{a_{n}a_{n-1}...a_{1}(a_{0}+1)}$ and the sum will be $2(a_{n}+a_{n-1}+...+a_{1}+a_{0})+1$ .)

Now, we now that the two first (and last) pages of the second chapter must be $\overline{ab9}$ and $\overline{a(b+1)0}$ such that $a+b+9+a+b+1 = 18 \Rightarrow a+b = 4$ . Since the total number of pages is $225$ the only solutions are $a=0, b=4$ and $a=1, b=3$ i.e. pages $(49,50)$ and $(139,140)$ hence the number of pages of the second chapter is $140-49+1 = 92$ .