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 the pendulum clock, which 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 for every 24 hours that pass, the clock shows 24 hours and 1 minute.

2. **Determine the Total Gain in Minutes for a Full Cycle**: Since the clock has a 12-hour dial, we need to find out how many minutes it will take for the clock to gain a full 12 hours (or 720 minutes).

3. **Calculate the Time Taken to Gain 720 Minutes**:
- The clock gains 1 minute every day.
- To find out how many days it will take to gain 720 minutes, we can set up the equation:
\[ \text{Days} = \frac{\text{Total Gain in Minutes}}{\text{Gain per Day}} = \frac{720 \text{ minutes}}{1 \text{ minute/day}} = 720 \text{ days} \]

4. **Conclusion**: Therefore, it will take 720 days for the pendulum clock to indicate the correct time again after being set correctly.

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

---