Question

On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?

• A. 51
• B. 49
• C. 50
• D. 55

Hint:

In clock problems, consider the relative speeds of the hands and the time intervals to calculate the number of crossings. Here, the second-hand crosses the minute-hand once per minute.

Answer 1

The Correct Option is C

Step 1: Understand the motion of the second and minute hands. The second-hand completes one full revolution (360 degrees) in 60 seconds, while the minute-hand completes one revolution in 3600 seconds (1 hour). Step 2: Calculate the crossings in one minute. In one minute, the second-hand crosses the minute-hand exactly once. Step 3: Calculate the crossings between 12:05:00 and 12:55:00. The time interval between 12:05:00 and 12:55:00 is 50 minutes. Hence, the second-hand and minute-hand will cross each other exactly 50 times during this period. Step 4: Conclusion. The total number of crossings is \( 50 \).