A clock is started at 12 o'clock noon. By 10 minutes past 5, the hour hand has turned through

Options

A. a. 145 degree
B. b. 150 degree
C. c. 155 degree
D. d. 160 degree

Answer

To solve the problem, we need to determine how much the hour hand of a clock has turned from 12 o'clock noon to 5:10 PM.

### Step-by-Step Solution:

1. **Calculate the total time from 12:00 to 5:10:**
- From 12:00 to 5:00 is 5 hours.
- From 5:00 to 5:10 is an additional 10 minutes.
- Therefore, the total time is 5 hours and 10 minutes.

2. **Convert the total time into hours:**
- 10 minutes can be converted into hours:
\[ 10 \text{ minutes} = \frac{10}{60} \text{ hours} = \frac{1}{6} \text{ hours} \]
- So, the total time in hours is:
\[ 5 \text{ hours} + \frac{1}{6} \text{ hours} = \frac{30}{6} + \frac{1}{6} = \frac{31}{6} \text{ hours} \]

3. **Determine the angle turned by the hour hand in one hour:**
- The hour hand completes a full circle (360 degrees) in 12 hours.
- Therefore, the angle turned by the hour hand in one hour is:
\[ \frac{360 \text{ degrees}}{12} = 30 \text{ degrees} \]

4. **Calculate the total angle turned by the hour hand in \(\frac{31}{6}\) hours:**
- The angle turned by the hour hand in \(\frac{31}{6}\) hours is:
\[ \text{Angle} = 30 \text{ degrees/hour} \times \frac{31}{6} \text{ hours} = \frac{30 \times 31}{6} \text{ degrees} \]
- Simplifying this gives:
\[ = \frac{930}{6} = 155 \text{ degrees} \]

5. **Conclusion:**
- The hour hand has turned through **155 degrees** by 10 minutes past 5.