A watch reads 3 : 30. If the minute hand points towards the north-east direction, then in what direction will the hour hand point?/ एक घड़ी में `3 : 30` बजे हैं। यदि मिनट की सुई उत्तर-पूर्व की ओर है, तो घंटे की सुई किस दिशा में होगी?

Options

A. South - West/ दक्षिण-पश्चिम
B. North - West/ उत्तर-पश्चिम
C. South - east/ दक्षिण-पूर्व
D. North- east/ उत्तर-पूर्व

Explanation

To determine the direction in which the hour hand points when the watch reads 3:30 and the minute hand points towards the north-east, we can follow these steps:

### Step 1: Understand the Position of the Clock Hands
At 3:30:
- The minute hand is on the 6 (which represents 30 minutes).
- The hour hand is halfway between the 3 and the 4.

### Step 2: Determine the Angle of the Minute Hand
Since the minute hand points towards the north-east:
- North-east is at a 45-degree angle from the north.
- Therefore, the minute hand is positioned at 45 degrees from the north.

### Step 3: Calculate the Position of the Hour Hand
The hour hand moves as follows:
- Each hour represents 30 degrees (360 degrees / 12 hours).
- At 3:00, the hour hand is at 90 degrees (3 hours × 30 degrees).
- At 3:30, the hour hand moves an additional 15 degrees (half of 30 degrees) towards the 4 o'clock position.

Thus, the hour hand at 3:30 is at:
- 90 degrees + 15 degrees = 105 degrees.

### Step 4: Determine the Direction of the Hour Hand
Now we need to find out where the hour hand points:
- The hour hand at 105 degrees is between the 3 o'clock (90 degrees) and the 4 o'clock (120 degrees) positions.
- Since the minute hand is at north-east (45 degrees), we can visualize the clock:
- North is at 12 o'clock,
- East is at 3 o'clock,
- South is at 6 o'clock,
- West is at 9 o'clock.

### Step 5: Identify the Direction
Given that the hour hand is at 105 degrees, which is slightly more than 90 degrees (east), it points towards the north-west direction.

Thus, the hour hand points towards the **north-west** direction.

### Final Answer
The hour hand points towards the **north-west** direction.

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