Question

at what time from 8 to 9 the hands of the clock are in opposite direction
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Answer 1

Given : A clock time between 8 & 9

To Find : at what time from 8 to 9 the hands of the clock are in opposite direction

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Solution:

At 8 o clock

Hour hand is  at  ( 8/12) * 360 = 240°

Minute Hand is at 0°

Now  hands of the clock to be in opposite direction

Angle between them = 180°

If Hour Hand moves x°  Then Minute hand should move (60 + x)°

Minute hand moved 360°  in 60  minutes

=> 6° in 1 Minute

Hour Hand moves 360° in 12 Hr

Hour Hand moves 30° in 1 Hr

Hence 0.5°  in 1 minute

Hour hand moves 1° in 2 Minutes

=> Hour hand moves x°  in 2x  minutes

Minute hand moved  in 2x minutes  =  6 * 2x = 12x°

12x° =  (60 + x)°

=> 11x = 60

=> x = 60/11

2x = 120/11  minutes = 10.91  minutes ≈ 11 minutes

At 8 hr 11 Minutes  hands of the clock are in opposite direction

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