Time, Speed and Distance Question 1 - CAT 2023
The minor angle between the hours hand and minutes hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8.48 am when this angle increases by 50% is:
Step-by-Step Explanation
Find the initial position at 8:48 am:
Every hour mark on a clock represents 30°, and the hour hand moves at 0.5° per minute.
Hour Hand Position = (8 × 30°) + (48 × 0.5°)
= 240° + 24°
= 264°
The minute hand moves at 6° per minute.
Minute Hand Position = 48 × 6° = 288°
Initial Angle = 288° − 264° = 24°
Calculate the target change:
The angle needs to increase by 50% of its current value:
Required Increase = 50% of 24° = 12°
Determine the time duration (m):
The relative speed between the minute hand and the hour hand is:
6° − 0.5° = 5.5° = 11/2° per minute
Time (m) = Required Increase / Relative Speed
= 12/(11/2) = 24/11 minutes
Correct Option: D
💡 FundaMakers Tip:
Do not waste time calculating absolute hand positions from scratch if you can remember the relative angle formula: θ = |30H − 5.5M|. For H = 8 and M = 48, we get θ = |240 − 264| = 24°. Since the hands are moving forward, any further separation occurs at the constant relative rate of 11/2° per minute. Keep this tracking rate memorized for all clock problems!