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 a given minute, the second-hand and minute-hand cross each other approximately once, but the exact time of crossing changes slightly. In a 50-minute span, they will cross 51 times.

Answer 1

The Correct Option is A

Step 1: Understanding the clock hand movements. The second-hand of a clock moves 360° in one minute, completing one revolution per minute. The minute-hand moves 360° in 60 minutes, completing one revolution per hour. Step 2: How often do the hands cross? The second-hand and minute-hand cross each other approximately once every minute. However, the time they meet is slightly different in each cycle. Step 3: Determine how many times they cross from 12:05:00 to 12:55:00. This is a 50-minute span (from 12:05 to 12:55). The second-hand and minute-hand cross 51 times during this period. Final Answer: The second-hand and minute-hand cross each other 51 times during the time from 12:05:00 to 12:55:00.