The angle between the hour hand and the minute hand of a clock at 10 m

The angle between the hour hand and the minute hand of a clock at 10 minutes past 3 is

30°
35°
37.5°
40°
This question was previously asked in
UPSC CAPF – 2018
The angle between the hour hand and the minute hand of a clock at 10 minutes past 3 is 35°.
– The minute hand moves 360 degrees in 60 minutes, so its speed is 6 degrees per minute (360/60).
– The hour hand moves 360 degrees in 12 hours (720 minutes), so its speed is 0.5 degrees per minute (360/720).
– At 3:10, the time is 3 hours and 10 minutes past 12 o’clock.
– Position of the minute hand: At 10 minutes, the minute hand is at 10 * 6 = 60 degrees from the 12 o’clock mark.
– Position of the hour hand: At 3 hours and 10 minutes, the hour hand’s position relative to 12 o’clock is (3 hours * 30 degrees/hour) + (10 minutes * 0.5 degrees/minute) = 90 + 5 = 95 degrees from the 12 o’clock mark. (Note: Each hour mark is 30 degrees apart: 360/12 = 30).
– The angle between the hands is the absolute difference between their positions: |95° – 60°| = 35°.
Clock problems involve calculating the relative positions of the hour and minute hands based on their speeds. The hour hand moves continuously, not just jumping from one hour mark to the next.