Question 30
For positive 2-digit integers $x$ and $y$, the ten's digit of $x$ equals the one's digit of $y$ and the ten's digit of $y$ equals the one's digit of $x$. Let $P$ be the product of $x$ and $y$. Suppose $P$ is a 4-digit number, and suppose that the 2-digit number given by the last (i.e., the bottom) 2 digits of $P$ is 23 greater than the 2-digit number given by the first (i.e., the top) 2 digits of $P$. Determine the value of $P$.