At what time between 2 o’clock and 3 o’clock will the hour and minute hands of a clock be 12 minutes division apart?
12 minutes past 2 o'clock
18 minutes past 2 o'clock
24 minutes past 2 o'clock
30 minutes past 2 o'clock
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2018
The minute hand moves 6 degrees per minute. The hour hand moves 0.5 degrees per minute. The relative speed of the minute hand with respect to the hour hand is 5.5 degrees per minute.
At 2:00, the hour hand is at 60 degrees from 12 (2 * 30), and the minute hand is at 0 degrees. The hour hand is 60 degrees ahead of the minute hand.
We want the difference in angles to be 72 degrees. This can be when the minute hand is 72 degrees behind the hour hand, or 72 degrees ahead.
Let ‘t’ be the time in minutes past 2.
Angle of minute hand = 6t.
Angle of hour hand = 60 + 0.5t.
We want |6t – (60 + 0.5t)| = 72.
|5.5t – 60| = 72.
Case 1: 5.5t – 60 = 72 => 5.5t = 132 => t = 132 / 5.5 = 1320 / 55 = 24.
Case 2: 5.5t – 60 = -72 => 5.5t = -12 => t = -12 / 5.5, which is not possible for time after 2:00.
So, the time is 24 minutes past 2 o’clock. At 2:24, the minute hand is at 24 * 6 = 144 degrees. The hour hand is at 60 + 24 * 0.5 = 60 + 12 = 72 degrees. The difference is 144 – 72 = 72 degrees, which is 12 minute divisions (72/6).