At a railways 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 step by step, we will follow these calculations:

### Step 1: Determine the time lost by the watch in one day.
The watch loses 3 minutes in 4 hours. We need to find out how much time it loses in 24 hours.

\[ \text{Time lost in 24 hours} = \left(\frac{3 \text{ minutes}}{4 \text{ hours}}\right) \times 24 \text{ hours} \]

Calculating this gives:

\[ \text{Time lost in 24 hours} = \frac{3 \times 24}{4} = 18 \text{ minutes} \]

### Step 2: Calculate how many days it will take for the watch to show the correct time again.
The watch is set correctly on Sunday noon. Since it loses 18 minutes each day, we want to find out how many days it will take for the watch to lose a total of 24 hours (which is 1440 minutes).

We can set up the equation:

\[ \text{Total time lost} = \text{Time lost per day} \times \text{Number of days} \]

Substituting the known values:

\[ 1440 \text{ minutes} = 18 \text{ minutes/day} \times \text{Number of days} \]

Now, solving for the number of days:

\[ \text{Number of days} = \frac{1440}{18} = 80 \]

### Step 3: Determine when the watch will show the correct time again.
Since the watch was set correctly on Sunday noon, we need to add 80 days to Sunday noon.

Starting from Sunday noon, adding 80 days:

- 7 days make a week, so 80 days is equivalent to \( \frac{80}{7} = 11 \) weeks and 3 days.

Thus, 80 days from Sunday noon will be:

- 11 weeks from Sunday brings us back to Sunday noon.
- Adding 3 more days brings us to Wednesday noon.

### Final Answer:
The watch will show the correct time again on **Wednesday noon, 80 days after it was set correctly on Sunday noon**.