JNU SSS 2010 Question 33: Sets, relations and functions

Let $X_1$, $X_2$, $\cdots$, $X_{20}$ and $Y_1$, $Y_2$, $\cdots$, $Y_n$ be two collections of sets. Suppose every $X_i$ contains 5 elements and every $Y_j$ contains 2 elements and $\bigcup_{i=1}^{20} X_i = S = \bigcup_{j=1}^{n} Y_j$. If each element of $S$ belongs to exactly 10 of the $X_i$s and to exactly 4 of the $Y_j$s, then $n$ is