A wall-clock takes 9 seconds in tringing at 9 O'clock. The time it will take in tringing at 11 O'clock, is

Options

A. 10 seconds
B. 11 seconds
C. 11.25 seconds
D. 10.80 seconds

Answer

To solve the problem, we need to determine how long it will take for the wall-clock to ring at 11 o'clock, given that it takes 9 seconds to ring at 9 o'clock.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- At 9 o'clock, the clock rings 9 times and takes 9 seconds.
- We need to find out how long it will take for the clock to ring at 11 o'clock.

2. **Determine the Number of Intervals**:
- When the clock rings 9 times, it creates 8 intervals (the time between each ring).
- Therefore, for 9 rings, the number of intervals = 9 - 1 = 8.

3. **Calculate the Duration of Each Interval**:
- Since the clock takes 9 seconds for 8 intervals, the duration of one interval can be calculated as:
\[ \text{Duration of one interval} = \frac{9 \text{ seconds}}{8 \text{ intervals}} = \frac{9}{8} \text{ seconds} \]

4. **Determine the Number of Rings at 11 O'clock**:
- At 11 o'clock, the clock rings 11 times.
- The number of intervals for 11 rings = 11 - 1 = 10.

5. **Calculate the Total Time for 11 Rings**:
- The total time for 10 intervals at 11 o'clock can be calculated as:
\[ \text{Total time} = \text{Number of intervals} \times \text{Duration of one interval} = 10 \times \frac{9}{8} \]
- Simplifying this:
\[ \text{Total time} = \frac{90}{8} = \frac{45}{4} = 11.25 \text{ seconds} \]

6. **Final Answer**:
- Therefore, the time it will take for the clock to ring at 11 o'clock is **11.25 seconds**.