Question

A clock is so placed that at 12 noon its minute hand points towards north-east. In which direction does its hour hand point at 1:30 pm?

• A. North
• B. South
• C. East
• D. West
• E.

Hint:

When solving clock-related problems, visualize the clock's positions and the corresponding directions carefully based on the given scenario.

Answer 1

The Correct Option is C

At 12 noon, the minute hand points towards north-east, which means the hour hand is pointing directly at 12 o'clock. 
At 1:30 pm, the hour hand will be halfway between 1 and 2 o'clock. This will place the hour hand at a 45-degree angle, which corresponds to the East direction. Hence, the correct answer is (c) East. 

Answer 2

Work out the clock's rotation offset first, then apply it to the hour hand's normal position.

1. Step 1: On a normally oriented clock, the minute hand at 12 points to 12, corresponding to North. Here it points to North-East instead, a rotation of 45 degrees clockwise from the standard orientation.
2. Step 2: The hour hand moves 30 degrees per hour. At 1:30, it has moved 1.5 hours from 12, i.e. \( 1.5 \times 30^{\circ} = 45^{\circ} \) clockwise from the 12 position, which on a standard clock corresponds to North-East.
3. Step 3: Adding the clock's own 45 degree clockwise rotation to the hour hand's normal 45 degree bearing gives \( 45^{\circ} + 45^{\circ} = 90^{\circ} \) clockwise from North, which is East.

Checking the options: North and South do not correspond to a 90 degree clockwise rotation from North, and West would correspond to 270 degrees, not 90; only East matches the result.

Hence, the correct answer is East.