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

### Concept & Logic When a clock rings a certain number of times, the time taken is measured by the *intervals* between the rings, not the rings themselves. To ring $n$ times, there are $(n-1)$ intervals. Assume each interval takes the same amount of time. ### Step-by-Step Solution 1. **Analyze 9 O'clock:** At 9 O'clock, the clock rings 9 times. Number of intervals = $9 - 1 = 8$ intervals. Time taken for 8 intervals = 9 seconds. Time taken for 1 interval = $\frac{9}{8}$ seconds. 2. **Analyze 11 O'clock:** At 11 O'clock, the clock rings 11 times. Number of intervals = $11 - 1 = 10$ intervals. 3. **Calculate Total Time:** Time for 10 intervals = $10 \times (\text{Time for 1 interval})$ $$Time = 10 \times \frac{9}{8}$$ $$Time = \frac{90}{8}$$ $$Time = \frac{45}{4} = 11.25\text{ seconds}$$ ### Exam Strategy & Shortcut Set up a direct proportion using intervals. $$ \frac{\text{Time}_1}{\text{Intervals}_1} = \frac{\text{Time}_2}{\text{Intervals}_2} $$ $$ \frac{9}{8} = \frac{x}{10} $$ $$ x = \frac{90}{8} = 11.25 $$ ### Common Pitfall The most common mistake is dividing the time by the number of rings (e.g., $9/9 = 1$ second per ring) and then multiplying by the new number of rings ($1 \times 11 = 11$ seconds). Always count the gaps (intervals) between the strikes. ### Final Answer Therefore, the correct answer is **11.25 seconds**.