Been stuck on the question for a few days and any leads would be greatly appreciated. My thought process was for arbitrary element $x \in X$, let there be $g$ near parallel classes. These near parallel classes are blocks of size $\frac{v-1}{k}$ since they partition $X \backslash \{x\}$. Proving $g= \frac{r}{v-1}$ is also equivalent to showing $g= \frac{\lambda}{k-1}$ by various properties of bibd's. I feel the second representation can be used to prove the statement somehow by the relationship of the elements within the blocks of the near parallel classes with deficient point x, but can't figure out how to proceed from here. The question is from "Combinatorial Designs: Constructions and Analysis" if that helps any. Thank you.
If $(X,A)$ is a $(v,k, \lambda)$ BIBD, a near parallel class in $(X,A)$ is a subset of disjoint blocks from $A$ whose union is $X \backslash \{x\}$ for some point $x\in X$ where $x$ is called a deficient point of the near parallel class. A partition of $A$ into near parallel classes is called a near resolution, and $(X,A)$ is said to be near resolvable if $A$ has at least one near solution.