Between 5 am and 5 pm of a particulanday for how many times are the minute and the hour hands together ?

Options

A. 11
B. 22
C. 33
D. 44

Answer

To determine how many times the minute and hour hands of a clock are together between 5 AM and 5 PM, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Clock Mechanics**:
The minute hand completes one full revolution (360 degrees) in 60 minutes, while the hour hand completes one full revolution in 12 hours (720 minutes).

2. **Finding the Frequency of Coincidence**:
The minute and hour hands are together 11 times in a 12-hour period. This is because they coincide once every 65.45 minutes on average.

3. **Time Interval**:
The time interval from 5 AM to 5 PM is 12 hours.

4. **Counting the Coincidences**:
Since the hands coincide 11 times in a 12-hour period, we can conclude that between 5 AM and 5 PM, the minute and hour hands will be together 11 times.

5. **Final Answer**:
Therefore, the minute and hour hands are together **11 times** between 5 AM and 5 PM.