Question

Two hands of an ordinary clock lie exactly over one another how many times in a continuous period of 72 hours?

• A. 24 times
• B. 72 times
• C. 76 times
• D. 66 times
• E. 56 times

Hint:

The hands overlap 11 times in every 12-hour period (not 12 times, because the overlap at 12:00 is counted as the start of the next cycle).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The hour and minute hands of a clock overlap once every 65 \(\frac{5}{11}\) minutes. In a 12-hour period, they overlap 11 times.

Step 2: Calculation for 72 Hours:
In 12 hours, the hands overlap 11 times.
For 72 hours, which is \(72/12 = 6\) cycles of 12 hours.
Total number of overlaps = \(11 \times 6 = 66\) times.

Step 3: Final Answer:
The hands lie exactly over one another 66 times in 72 hours.