At what time between `9` O'clock and `10` O'clock are the hands of a clock in the opposite direction ?

Options

A. 15 minutes past 9
B. 16 minutes past 9
C. `16(4)/(11)` minutes past 9
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 . 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) 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.