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.

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