CAT 2023 Slot 1 QA Question & Solution
ArithmeticMedium
Question
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
Options
$\frac{36}{11}$
2
4
$\frac{24}{11}$
Solution
The given time is 8:48 AM.
Angle made by hours hand w.r.t 12 is 8 * 30 (30 degrees in 1 hour) + 0.5 * 48 (0.5 degree in 1 minute) = 240 + 24 = 264 degrees.
Angle made by minutes hands w.r.t 12 is 48 * 6 = 288 degrees.
=> The angle between them is 288 - 264 = 24 degrees.
This should further increase by 12 degrees (50% of 24)
After m minutes, the further increase in angle = (6 - 0.5)*m = $\dfrac{11}{2}m=12$ => m = $\dfrac{24}{11}$