The Hasty Wristwatch
A perfect clock has its hour and minute hands coincide every 720/11 minutes of its own time. A faulty wristwatch, whose two hands still move in the correct 12:1 ratio, is observed to have its hands coincide every 65 minutes of true time. How many minutes does the watch gain over 24 hours of true time? Give the exact answer as a reduced improper fraction, or as a decimal rounded to 2 or 3 places.
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Source: Classic clock-hand riddle (the watch whose hands meet at the wrong interval) in wide circulation; no traceable original source. Statement written for AxiomIQ.