A swiss watch is being shown in a museum which has a very peculiar property. It gains as much in the days as it loses during night between 8 pm to 8 am. In a week how many times will the clock show the correct time?

Options

A. 6 times
B. 14 times
C. 7 times
D. 8 times

Answer

To solve the problem, we need to analyze the behavior of the Swiss watch during the day and night cycles.

### Step-by-Step Solution:

1. **Understanding the Time Gain and Loss**:
- The watch gains time during the day and loses an equal amount of time during the night.
- The night period is from 8 PM to 8 AM, which is a total of 12 hours.

2. **Day and Night Cycle**:
- During the day (from 8 AM to 8 PM), the watch gains time.
- During the night (from 8 PM to 8 AM), the watch loses the same amount of time that it gained during the day.

3. **Correct Time Display**:
- Since the watch loses time at night, there will be a moment during the day when the watch shows the correct time.
- This will happen once every day because the gain during the day compensates for the loss at night.

4. **Counting the Days in a Week**:
- In one week, there are 7 days.
- Since the watch shows the correct time once each day, it will show the correct time 7 times in those 7 days.

5. **Including the Start Time**:
- The problem states that we start observing the time from 8 PM.
- At 8 PM on the first day, the watch will also show the correct time because it resets to the correct time at that moment.

6. **Total Correct Time Instances**:
- Therefore, in one week, the watch will show the correct time 7 times (once each day) plus 1 additional time at the start (8 PM on the first day).
- This gives a total of 7 + 1 = 8 times.

### Final Answer:
The Swiss watch will show the correct time **8 times** in a week.

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