The correct word problem that has a solution of |−25|=25 is:
"Martin received his September salary on the 30th day. He was paid $500. The day after, his boss realized that he made a mistake in Martin’s pay and gave Martin an additional $25. What is the magnitude of Martin’s salary adjustment?"
This problem involves calculating the magnitude of a change in salary, which relates to the absolute value concept, as the adjustment can be seen as a change of -$25 (for the mistake) and +$25 (for the correction), resulting in |−25|=25.