My watch was 8 minutes behind at 8 pm on Sunday but within a week at 8 pm on Wednesday it was 7 minutes ahead of time. During this period at which time this watch has shown the correct time :

Options

A. Tuesday 10 : 24 am
B. Wednesday 9 : 16 pm
C. It cannot show the correct time during this period
D. None of the above

Answer

To solve the problem, we need to determine when the watch showed the correct time between Sunday at 8 PM and Wednesday at 8 PM. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the time duration from Sunday to Wednesday
From Sunday at 8 PM to Wednesday at 8 PM is a total of 3 days.

- **Calculation**:
\[ \text{Total time} = 3 \text{ days} = 3 \times 24 \text{ hours} = 72 \text{ hours} \]

### Step 2: Determine the time discrepancies
Initially, the watch was 8 minutes behind at 8 PM on Sunday and 7 minutes ahead at 8 PM on Wednesday.

- **Calculation**:
\[ \text{Total change in time} = 8 \text{ minutes (behind)} + 7 \text{ minutes (ahead)} = 15 \text{ minutes} \]

### Step 3: Calculate the effective time gained by the watch
The watch gained a total of 15 minutes over the 72 hours.

### Step 4: Calculate the speed of the watch
The speed of the watch can be calculated based on the total time gained over the total duration.

- **Calculation**:
\[ \text{Speed of the watch} = \frac{15 \text{ minutes}}{72 \text{ hours}} = \frac{15}{72} \text{ minutes per hour} = \frac{5}{24} \text{ minutes per hour} \]

### Step 5: Determine when the watch was correct
To find when the watch showed the correct time, we need to determine how long it takes for the watch to cover the initial 8 minutes it was behind.

- **Calculation**:
\[ \text{Time to cover 8 minutes} = \frac{8 \text{ minutes}}{\text{Speed of the watch}} = \frac{8}{\frac{5}{24}} = 8 \times \frac{24}{5} = \frac{192}{5} = 38.4 \text{ hours} \]

### Step 6: Add the time taken to the initial time
Now, we add the time taken to the initial time of Sunday at 8 PM.

- **Calculation**:
\[ 8 \text{ PM on Sunday} + 38.4 \text{ hours} = 8 \text{ PM} + 38 \text{ hours} + 24 \text{ minutes} \]
- 38 hours from 8 PM on Sunday brings us to 10 AM on Tuesday (24 hours to Monday 8 PM, then 14 hours to Tuesday 10 AM).
- Adding 24 minutes gives us 10:24 AM on Tuesday.

### Final Answer
The watch showed the correct time at **10:24 AM on Tuesday**.

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