How many times in a day are the hands of a clock pointing opposite to each other?
Explanation
Solution
1. Understanding the Frequency
In every 12-hour period, the minute hand and the hour hand point in opposite directions (180∘ apart) exactly 11 times.
2. The "Missing" Occurrence
You might expect it to happen 12 times, but there is a "overlap" or shared point. Between 5:00 and 7:00, the hands are opposite only once, which occurs exactly at 6:00. Because this single event covers two hour-slots, we lose one occurrence per 12-hour cycle.
3. Mathematical Calculation
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In 12 hours, the hands are opposite: 12−1=11 times.
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In a full day (24 hours), the hands are opposite: 11×2=22 times.
4. Final Answer
The hands of a clock point in opposite directions 22 times in a day.
Correct Option: C) 22
