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?

Options

A. a) 15 minutes past 9
B. b) 16 minutes past 9
C. c) `16 (4)/(11)` minutes past 9
D. d) `17 (1)/(11)` minutes past 9

Answer

C

Explanation

At 9 O.clock, the minute hand is `9 xx 5=45` minute- spaces behind the hour hand. Thereforce, the minute hand will have to gain `45-30=10` minute space over the hour hand.
`because` Gain of 55 minute spaces equals 60 minutes.
`therefore` Gain of 15 minute spaces equals
`=(60)/(55) xx 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.