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:

When calculating the number of times hands of a clock cross, remember that they typically cross once every minute except when aligned at the top of the hour.

Answer 1

The Correct Option is C

The second-hand and minute-hand of a clock cross each other every time the second-hand laps the minute-hand. Since the second-hand moves significantly faster than the minute-hand, this occurs more frequently than once per minute. Step 1: Calculate the frequency of crossings. Every hour, the second-hand and minute-hand cross each other 59 times as the minute-hand moves slowly away from each crossing point at a slower rate than the second-hand. Step 2: Determine the time interval. The time interval from 12:05:00 to 12:55:00 is 50 minutes. Since there is one crossing near the start of each minute, and we start counting from just after the 5th minute of the hour, we include all crossings from the 6th minute to the 55th minute. Step 3: Count the crossings. \[ \text{Total crossings} = 55 - 5 = 50 \text{ crossings} \] Thus, there are 50 crossings during the specified time period. Conclusion.
The number of times the second-hand and the minute-hand cross each other from 12:05:00 to 12:55:00 is \( \mathbf{50} \).