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: The hour and minute hands coincide 11 times every 12 hours.
Step 2: Time difference: From 10:20 AM March 8 to 10:20 AM March 11 = 72 hours. Then from 10:20 AM to 11:15 AM on March 11 = 55 minutes. Total time = 72 hours + 55 minutes = 72.9167 hours.
Step 3: Number of 12-hour periods = $72.9167 \div 12 \approx 6.0764$ periods.
Step 4: In each 12-hour period, hands coincide 11 times. So total coincidences = $6 \times 11 = 66$ coincidences in the full 72 hours.
Step 5: The remaining 55 minutes is less than 65.45 minutes between coincidences, so no additional coincidence.
Step 6: Final Answer: 66 times.