After 9^ 0 clock at what time between 9 p.m. and 10 p.m. will the hour and minute hands of a clock point in opposite direction?

Step-by-step solution

At 9 O'clock, the minute hand is 9 5=45 minute - spaces behind the hour hand. Therefore, the minute hand will have to gain 45-30=10 minute space over the hour hand. ∵ Gain of 55 minute spaces equals 60 minutes. ∴ Gain of 15 minute spaces equals = 60 55 15= 180 11 =16 4 11 Therefore, hour and minute hands of a clock point in opposite direction after 9 O'clock at 16 4 11 minutes past 9.