RAS question
What is the angle between the hour hand and the minute hand at 4:30?
Correct answer: (D) 45°.
At 4:30, the smaller angle between the hour hand and the minute hand is 45°.
Explanation
At 4:30, the minute hand is on 6, which is 180° from 12 because each minute space on a clock is 6°. The hour hand is not fixed at 4; by 4:30 it has moved halfway from 4 towards 5. Its position is 4 × 30° plus 30 × 0.5°, giving 120° + 15° = 135°. The angle between the two hands is therefore 180° − 135° = 45°. This matches SATHEE's clock-angle rule, which uses the hour hand's 0.5° per minute movement and the minute hand's 6° per minute movement, so the hour hand's advance after 4 o'clock must be included.
Why the other options are wrong
- (A) 75° comes from overestimating the separation; once the hour hand's 15° movement after 4 o'clock is included, the gap from the minute hand at 180° is only 45°.
- (B) 60° would ignore the exact halfway movement of the hour hand between 4 and 5, but at 4:30 the hour hand is at 135°, not at a position that leaves a 60° gap.
- (C) 30° understates the separation because the minute hand is at 180° while the hour hand is at 135°, leaving 45° between them.
Concept
This tests clock-angle reasoning in the Reasoning and Mental Ability syllabus. It recurs in RAS because it combines a simple circular scale with relative hand movement, a common pattern in mental calculation questions.