The current time is 10 minutes past 3 in the afternoon. What will be the angle between the hour hand and the minute hand of the clock, 4 hours and 30 minutes from now?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10°
The hour hand turns 30° every hour and so 0.5° every minute; the minute hand turns 6° every minute. Measuring both from 12, the angle between the hands is the difference of the two readings.
Time after 4 hours 30 minutes: 3:10 p.m. + 4:30 \(=\) 7:40 p.m.
Hour hand at 7:40: \(7\times30+40\times0.5=210+20=230^\circ\) from 12
Minute hand at 40 minutes: \(40\times6=240^\circ\) from 12
Angle between them: \(240-230=10^\circ\)
