A watch, which gains time uniformly, was 5 minutes behind the correct time when it showed 11:55 AM on Monday. It was 10 minutes ahead of the correct time when it showed 06:10 PM on the next day. When did the watch show the correct time?

Options

A. 6 AM, Tuesday
B. 6 PM, Monday
C. 2 PM, Tuesday
D. 10 PM, Monday

Answer

To solve the problem step-by-step, we need to analyze the information given about the watch's time gain and the corresponding correct times.

### Step 1: Understand the initial conditions
The watch was 5 minutes behind the correct time when it showed 11:55 AM on Monday. This means that the correct time at that moment was:
- **Correct Time = 11:55 AM + 5 minutes = 12:00 PM (Noon)**

### Step 2: Determine the time on the next day
The watch showed 6:10 PM on Tuesday and was 10 minutes ahead of the correct time at that moment. Therefore, the correct time was:
- **Correct Time = 6:10 PM - 10 minutes = 6:00 PM**

### Step 3: Calculate the time difference between the two observations
Now, we need to calculate the time difference between 12:00 PM on Monday and 6:00 PM on Tuesday:
- From **12:00 PM (Noon) on Monday** to **12:00 PM (Noon) on Tuesday** is **24 hours**.
- From **12:00 PM (Noon) to 6:00 PM** on Tuesday is an additional **6 hours**.
- Therefore, the total time from the first observation to the second observation is:
- **Total Time = 24 hours + 6 hours = 30 hours**

### Step 4: Calculate the total gain of the watch
The watch gained time from being 5 minutes behind to being 10 minutes ahead:
- Total gain = 5 minutes (to catch up) + 10 minutes (to get ahead) = **15 minutes** in **30 hours**.

### Step 5: Determine the rate of gain of the watch
To find out how much time the watch gains per hour:
- Gain per hour = Total gain / Total time = 15 minutes / 30 hours = **0.5 minutes per hour**.

### Step 6: Calculate when the watch shows the correct time
To find out when the watch shows the correct time, we need to determine how long it takes to gain the 5 minutes it was initially behind:
- Time to gain 5 minutes = 5 minutes / (0.5 minutes/hour) = **10 hours**.

### Step 7: Find the correct time when the watch shows the correct time
Starting from the initial correct time of 12:00 PM on Monday, we add 10 hours:
- **12:00 PM + 10 hours = 10:00 PM on Monday**.

### Final Answer
The watch showed the correct time at **10:00 PM on Monday**.

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