Discussion

What will be angle between the two hands of a clock at 10.25 pm?

Answer: C

The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is

\[ \theta = \left| 30H - 5.5M \right| \]

\[ \theta = \left| 30(10) - 5.5(25) \right| = \left| 300 - 137.5 \right| \]

\[ = 162.5^{\circ} \]

This is the smaller of the two angles; the reflex angle on the other side is \( 360 - 162.5 = 197.5^{\circ} \).

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