At what angle are the hour hand and the minute hand of a clock inclined at 15 minutes past 5?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(67\frac{1}{2}^\circ\)
Measure both hands from the 12. The minute hand turns 6° a minute (360° in 60 minutes). The hour hand turns 30° an hour, that is, ½° a minute, so at 15 minutes past 5 it has moved a quarter of the way from the 5 towards the 6.
Minute hand at 15 minutes: \(15\times6^\circ=90^\circ\)
Hour hand at 5:15: \(5\times30^\circ+15\times\frac{1}{2}^\circ=150^\circ+7\frac{1}{2}^\circ=157\frac{1}{2}^\circ\)
Angle between the hands \(=157\frac{1}{2}^\circ-90^\circ=67\frac{1}{2}^\circ\)
Tip: At H hours and M minutes the angle between the hands is \(\left|30H-\frac{11}{2}M\right|\) degrees (subtract from 360° if it comes to more than 180°). Here \(\left|150-82\frac{1}{2}\right|=67\frac{1}{2}^\circ\).