A certain pendulum clock with a 12 hr dial happens to gain 1 min/day. After setting the clock to the correct time how long it will take to indicate correct time again?

Answer

To solve the problem of how long it will take for a pendulum clock that gains 1 minute per day to indicate the correct time again after being set correctly, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Gain of the Clock**:
The clock gains 1 minute every day. This means that over time, the clock will show a time that is ahead of the actual time.

2. **Calculate the Total Minutes in 12 Hours**:
Since the clock has a 12-hour dial, we need to determine how many minutes are in 12 hours:
\[ 12 \text{ hours} = 12 \times 60 = 720 \text{ minutes} \]

3. **Determine How Long it Takes to Gain 720 Minutes**:
Since the clock gains 1 minute per day, we need to find out how many days it will take to gain a total of 720 minutes:
\[ \text{Days required} = \frac{720 \text{ minutes}}{1 \text{ minute/day}} = 720 \text{ days} \]

4. **Conclusion**:
After 720 days, the clock will have gained 12 hours and will show the correct time again.

### Final Answer:
It will take **720 days** for the clock to indicate the correct time again.

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