Watch India Corporation made a wrist watch in which the minute hand makes one complete round of dial in 12 minute and accordingly the hour hand too. When I have set this watch at 12:00 noon on Ist February this year. Which time will be shown by this watch at 3 O'clock on the same day.

Options

A. `2 : 30` P.M.
B. `6 : 15` A.M.
C. 3 O' clock
D. can't be determined

Answer

To solve the problem, we need to determine what time the Watch India Corporation's wristwatch will show after 3 hours have passed since it was set at 12:00 noon, given that the minute hand completes one full rotation in 12 minutes.

### Step-by-Step Solution:

1. **Understand the Watch's Mechanism**:
- The minute hand of the watch completes one full rotation (360 degrees) in 12 minutes.
- This means that in 12 minutes, the minute hand moves to the 12 o'clock position again.

2. **Calculate the Speed of the Minute Hand**:
- Since the minute hand completes one full rotation in 12 minutes, in 60 minutes (which is 1 hour), it will complete:
\[ \text{Number of rotations in 60 minutes} = \frac{60 \text{ minutes}}{12 \text{ minutes}} = 5 \text{ rotations} \]
- Therefore, the minute hand completes 5 hours in 1 hour of real time.

3. **Determine the Time Interval**:
- We are interested in the time from 12:00 noon to 3:00 PM, which is a total of 3 hours.

4. **Calculate the Effective Time on the Watch**:
- If 1 hour of real time corresponds to 5 hours on this watch, then in 3 hours of real time:
\[ \text{Effective time on the watch} = 3 \text{ hours} \times 5 = 15 \text{ hours} \]

5. **Determine the Time Shown by the Watch**:
- Starting from 12:00 noon, if we add 15 hours:
- 12:00 noon + 12 hours = 12:00 midnight (next day)
- Then, adding the remaining 3 hours gives us:
\[ 12:00 midnight + 3 \text{ hours} = 3:00 AM \]
- Therefore, the watch will show 3:00 AM.

### Final Answer:
The time shown by the Watch India Corporation's wristwatch at 3:00 PM on the same day will be **3:00 AM**.

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