A clock is fixed on a horizontal table. At 3 "pm" its minute hand is pointing towards North . At 3.40 "pm", the minute hand will point towards ?

Options

A. A . `60^(@)` south of west
B. B. South-west
C. C. `60^(@)` west of south
D. D. none of these

Answer

To solve the problem, let's break it down step by step.

### Step 1: Understand the Position of the Clock Hands at 3 PM
At 3 PM, the minute hand is pointing towards North. This means:
- North is at the 12 o'clock position on the clock.
- The hour hand is at the 3 o'clock position.

### Step 2: Determine the Movement of the Minute Hand
The minute hand moves 360 degrees in 60 minutes. Therefore, in 1 minute, it moves:
\[ \text{Degrees per minute} = \frac{360 \text{ degrees}}{60 \text{ minutes}} = 6 \text{ degrees per minute} \]

### Step 3: Calculate the Time from 3 PM to 3:40 PM
From 3 PM to 3:40 PM, there are 40 minutes.

### Step 4: Calculate the Total Degrees Moved by the Minute Hand
In 40 minutes, the minute hand will move:
\[ \text{Total movement} = 40 \text{ minutes} \times 6 \text{ degrees per minute} = 240 \text{ degrees} \]

### Step 5: Determine the New Position of the Minute Hand
Since the minute hand started at North (0 degrees), after moving 240 degrees clockwise, we can find its new position:
- 240 degrees clockwise from North (0 degrees) can be calculated as follows:
- 90 degrees is East
- 180 degrees is South
- 270 degrees is West
- 240 degrees is between South (180 degrees) and West (270 degrees).

### Step 6: Identify the Direction
To find the exact direction:
- 240 degrees is 60 degrees past South towards West. Thus, the minute hand points 60 degrees West of South.

### Final Answer
At 3:40 PM, the minute hand will point towards **60 degrees West of South**.

---