Question

In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?

• A. 11
• B. 12
• C. 144
• D. 2

Hint:

In a 12-hour clock, the second, minute, and hour hands coincide 11 times in a 12-hour period, not 12, because the first coincidence occurs at the starting point of the cycle.

Answer 1

The Correct Option is A

To determine how many times the second, minute, and hour hands coincide in a 12-hour period, let's break it down:
1. Understanding the situation:
- A 12-hour clock completes one full cycle every 12 hours.
- The second hand makes one full revolution every minute.
- The minute hand moves around the clock every hour.
- The hour hand takes 12 hours to complete a full revolution.
2. Coincidence of hands:
- In every hour, the second, minute, and hour hands coincide once. However, this is a special condition and doesn’t occur exactly at the hour. The hands move at different speeds, so their exact coincidence point moves with time.
- The hands will not coincide at the same time every hour but will align once in each 60-minute cycle.
3. Calculation:
- From 3 PM to 3 AM, we have a 12-hour span.
- In each hour, the hands will coincide once.
- Therefore, in a 12-hour period, the hands will coincide 11 times.
- This is because at 12:00 (midnight), the hands will already be coincident, so the next coincidence will be after 1 hour, and so on for 11 occurrences in total.
Hence, the correct answer is (A) 11.