Question

Anora sees the time on her perfectly working ordinary wrist watch at 10:20 AM on 8th of March, 2025 and the next occasion when she sees the time on her same watch is at 11:15 AM on 11th of March, 2025. Determine the number of times, the hour and minute hand of her watch would have been exactly over one another between the two times that Anora saw the time on her watch?

• A. 67
• B. 66
• C. 72
• D. 6
• E. 73

Hint:

The hands of a clock coincide 11 times in every 12-hour period. Use this to calculate the number of coincidences over a given time interval.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a standard clock, the minute and hour hands coincide exactly 11 times in every 12-hour period (22 times in 24 hours). This is because the overlap between 11:00 and 1:00 happens only once, at 12:00.
Step 2: Key Formula or Approach:
1. Total time elapsed = Final time - Initial time.
2. Total coincidences = (Full 24-hour days \(\times 22\)) + (coincidences in the remaining hours).
Step 3: Detailed Explanation:
Calculate the duration from 10:20 AM, 8th March to 11:15 AM, 11th March:
- From 10:20 AM, 8th March to 10:20 AM, 11th March = 3 full days (72 hours).
Number of coincidences = \( 3 \times 22 = 66 \).
- Remaining interval: 10:20 AM to 11:15 AM on 11th March.
The hands of a clock coincide once approximately every \( 1 \text{ hour } 5 \frac{5}{11} \text{ minutes} \).
Between 10:00 and 11:00, the hands coincide at approx 10:54 AM.
Since 10:54 AM falls between 10:20 AM and 11:15 AM, there is exactly 1 additional coincidence.
Total coincidences = \( 66 + 1 = 67 \).
Step 4: Final Answer:
The hands were over each other 67 times.