What is the angle in degree between the hour hand and the minute hand of a clock when the time it shows is 5:20 PM?
35°
40°
42°
45°
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CBI DSP LDCE – 2023
First, calculate the angle of the hour hand from the 12 o’clock position.
The hour hand moves 360° in 12 hours, or 30° per hour (360°/12).
It also moves due to the minutes past the hour. In 60 minutes, the hour hand moves 30°. So, in 1 minute, it moves $30°/60 = 0.5°$.
At 5:20, the time is 5 hours and 20 minutes past 12. The total time in minutes past 12 is $(5 \times 60) + 20 = 300 + 20 = 320$ minutes.
Angle covered by hour hand = $320 \times 0.5° = 160°$.
Alternatively, angle = (5 hours $\times$ 30°/hour) + (20 minutes $\times$ 0.5°/minute) = 150° + 10° = 160°.
Second, calculate the angle of the minute hand from the 12 o’clock position.
The minute hand moves 360° in 60 minutes, or 6° per minute (360°/60).
At 20 minutes past the hour, the minute hand is at the 20 minute mark.
Angle covered by minute hand = $20 \times 6° = 120°$.
The angle between the hour hand and the minute hand is the absolute difference between their positions.
Angle = $|160° – 120°| = 40°$.