The inhabitants of planet Rahu measure time in hours and minutes which are…
2023
The inhabitants of planet Rahu measure time in hours and minutes which are different from the hours and minutes of our earth. Their day consists of 36 hours with each hour having 120 minutes. The dials of their clocks show 36 hours. What is the angle between the hour hand and the minutes hand of a Rahuian clock when it shows a time of 9:48? [Rahuians measure angles in degrees the way we do on earth. But for them, the angle around a point is 720 degrees instead of 360 degrees.]
- A.
100 degree
- B.
50 degree
- C.
150 degree
- D.
200 degree
Attempted by 1 students.
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Correct answer: A
CONCEPT: On any clock-type dial, each hand's angular speed equals the total degrees spanning the full dial divided by the time the hand takes for one complete revolution. The angle between the two hands at a given instant is the absolute difference between each hand's own position (its speed multiplied by the elapsed time), measured from the same reference point.
APPLICATION: Apply this to the Rahuian dial, which spans 720 degrees in total, over 36 Rahuian hours, with 120 Rahuian minutes per hour.
The minute hand completes one full 720-degree revolution every 120 minutes, so its speed = 720 / 120 = 6 degrees per minute.
The hour hand completes one full 720-degree revolution every 36 hours, so its speed = 720 / 36 = 20 degrees per hour = 20 / 120 = 1/6 degree per minute.
At a time of 9:48 (9 hours and 48 minutes elapsed since 0:00), the minute hand's position = 48 x 6 = 288 degrees.
The hour hand's position = 9 x 20 + 48 x 1/6 = 180 + 8 = 188 degrees.
The angle between the hands = |288 - 188| = 100 degrees.
CROSS-CHECK: Using relative speed -- the minute hand gains on the hour hand at (6 - 1/6) = 35/6 degrees per minute. Elapsed Rahuian minutes since 0:00 = 9 x 120 + 48 = 1128. Total gain = 1128 x 35/6 = 6580 degrees. Reducing modulo 720 degrees (one full circle): 6580 - 9 x 720 = 6580 - 6480 = 100 degrees, confirming the result.