The angle between the hour hand and the minute hand of a clock, when time is 3 : 25, will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(47\frac{1}{2}^\circ\)
The minute hand moves 6° per minute (360° in 60 minutes). The hour hand moves 30° per hour, that is, \(\frac{1}{2}^\circ\) per minute, so at 3:25 it has moved past the 3. Both positions are measured from the 12:
Hour hand: \(3\times30^\circ+25\times\frac{1}{2}^\circ=90^\circ+12.5^\circ=102.5^\circ\)
Minute hand: \(25\times6^\circ=150^\circ\)
Angle between them \(=150^\circ-102.5^\circ=47.5^\circ=47\frac{1}{2}^\circ\)
Shortcut: The angle at H hours M minutes is \(\left|30H-\frac{11}{2}M\right|\):
\(\left|30\times3-\frac{11}{2}\times25\right|=\left|90-137.5\right|=47.5^\circ\)