CAT 2023 Slot 1 QA Question 12: The minor angle between the hour hand and minute 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

Question

The minor angle between the hour hand and minute 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

Accepted Answer

At 8:48, the hour hand has moved
$8 	imes 30 + 48 	imes 0.5 = 240 + 24 = 264^{\circ}$

The minute hand has moved
$48 	imes 6 = 288^{\circ}$

So the minor angle is
$288^{\circ} - 264^{\circ} = 24^{\circ}$

A 50% increase makes the angle $24^{\circ} 	imes 1.5 = 36^{\circ}$.

The minute hand gains