Find the time shown by the clock if the hour hand is between 8 and 9 and the minute hand is pointing in the exact opposite direction of the hour hand.

The hour hand covers 30 degrees in 1 hour or 0.5 degrees / min

The min hand covers 360 degrees in 1 hour of 6 degrees/ min

Hence, we can say that the the minute hand gains 6 - 0.5 = 5.5 degrees on hour hand, every minute.

At 8 pm the the hour hand will be ahead of minute hand by 30*8 = 240 degrees.

Hence, the minute hand will have to cover 60 degrees more w.r.t the hour hand for them to point in opposite direction/ for the angle between them to be 180 degrees. 

let x be the number of minutes taken by the minute hand to do the same. 

5.5x = 60 

x = 60/5.5 = 120/11 = 10 10/11