1965 AHSME Problems/Problem 15

We begin by converting both $25_b$ and $52_b$ to base $10$ . $25_b = 2b+5$ in base $10$ and $52_b = 5b+2$ base $10$ . The problem tells us that $5b+2 = 4b+10$ , yielding $\boxed{8}$ as our final answer.