At a railway station a 24 hour watch loses 3 minutes in 4 hours. If it is set correctly on Sunday noon when will the watch show the correct time?

Options

A. 6 pm after 40 days
B. 12 noon after 75 days
C. 12 pm after 100 days
D. 12 noon after 80 days

Answer

To solve the problem, we need to determine when a watch that loses time will show the correct time again after being set correctly. Here’s the step-by-step solution:

### Step 1: Understand the time loss of the watch
The watch loses 3 minutes every 4 hours.

### Step 2: Calculate the daily time loss
Since there are 24 hours in a day, we can find out how many 4-hour intervals are in a day:
\[ \text{Number of 4-hour intervals in a day} = \frac{24 \text{ hours}}{4 \text{ hours}} = 6 \]
Now, we multiply the number of intervals by the time lost in each interval:
\[ \text{Total time lost in a day} = 6 \times 3 \text{ minutes} = 18 \text{ minutes} \]

### Step 3: Calculate the total minutes in a day
There are 1440 minutes in a day (24 hours × 60 minutes):
\[ \text{Total minutes in a day} = 24 \times 60 = 1440 \text{ minutes} \]

### Step 4: Determine how many days it takes to lose a full day (1440 minutes)
To find out how many days it will take for the watch to lose a full 24 hours (1440 minutes), we divide the total minutes in a day by the daily loss:
\[ \text{Number of days to lose 1440 minutes} = \frac{1440 \text{ minutes}}{18 \text{ minutes/day}} = 80 \text{ days} \]

### Step 5: Determine when the watch will show the correct time again
The watch was set correctly on Sunday noon. After 80 days, we need to find out what day and time it will be:
- Starting from Sunday noon, adding 80 days:
- 80 days from Sunday will be 80 mod 7 = 2 days (since there are 7 days in a week).
- Therefore, 80 days from Sunday will land on a Tuesday.

So, the watch will show the correct time again on **Tuesday at noon**.

### Final Answer
The watch will show the correct time again on **Tuesday at noon after 80 days**.

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