Is it 9 o'clock now?
I. After half an hour, the minute and the hour hands of the clock will make an angle of exactly 90° with each other.
II. Exactly 15 minutes ago, the minute and the hour hands of the clock coincided with each other.

Using Statement I: If the time is 9 o'clock now then after 30 minutes ie at 9:30 the angle between the minute and hour hand cannot be 90°. So, now time is not 9 o'clock.
Using Statement II: If the time is 9 o'clock now then after 15 minutes before the hour and minute hand of the clock can never coincide with each other Instead they will have an angle of 7.5°. So, the time now is not 90°' clock.