If the hour-hand and the minute-hand of a clock coincide every 64 minutes, how much does the clock gain or lose everyday?
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60 min
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35 min
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33 8 11 m i n
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32 8 11 m i n
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62 8 11 m i n
The hands of a clock coincide every 65 and 5/11 minutes. If they coincide every 64 minutes, the clock is gaining time. The gain per 64 minutes is (65 and 5/11 - 64) = 1 and 5/11 = 16/11 minutes. Daily gain = (16/11) * (24 * 60 / 64) = 32 and 8/11 minutes.
Under normal conditions, the hands of a clock coincide every 720/11 minutes, which is 65 5/11 minutes. If this faulty clock coincides every 64 minutes, it is running fast because the interval is shorter than normal. The clock gains (720/11) - 64 = (720/11) - (704/11) = 16/11 minutes in every 64 minutes. Over a 24 hour day, there are (24 * 60) / 64 = 22.5 such intervals of 64 minutes. Multiplying this by the 16/11 minute gain per interval gives 360/11 minutes, which is 32 8/11 minutes gained everyday. The provided option D text is fragmented, but it corresponds to this correct value.