Question:

From morning 11 O’clock to evening 7 O’clock, how many times will the hour hand and minute hand overlap each other?

Updated On: Aug 14, 2025
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The Correct Option is C

Solution and Explanation

Step 1: Concept of clock hand overlaps.
In a 12-hour period, the hour and minute hands overlap 11 times. This happens approximately every \( \frac{12}{11} \) hours (\(\approx 1\) hour 5 minutes). Step 2: Time range from 11 AM to 7 PM.
From 11 AM to 7 PM is 8 hours.
However, we must count overlaps starting after 11 AM up to and including the overlap just before 7 PM. Step 3: Counting overlaps.
- Overlaps occur at roughly: 12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, and next at 7:35 (which is outside range).
- This gives \(\mathbf{7}\) overlaps in the given time frame. \[ \boxed{\text{Number of overlaps = 7.}} \]
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