Answer
(a) Yes
(b) Yes
Work Step by Step
(a) Given $12a=25b$ or $3\cdot4\cdot a=5^2\cdot b$, we can see that there are no common factors among the numeric parts on both sides, thus we can conclude that $12|b$ and $25|a$.
(b) Given $10x=9y$ or $2\cdot5\cdot x=3^2\cdot y$, we can see that there are no common factors among the numeric parts on both sides, thus we can conclude that $10|y$ and $9|x$.