Question

At what time after 7:00 pm will the hands of the clock be opposite to each other?

Answer 1

Just at 7.00pm the hour hand is at 7 and minute hand is at 12.

Each minute division makes 6∘ at the center. So at 7.00 pm a reflex angle of 210^∘ will be formed between hour hand and minute hand because the hour hand will be at 35 minute divisions ahead of minute hand.

Let x minute after 7.00pm the hands of the clock will be opposite to each other.Then the angle between the hands will be 180^∘

We know hour hand rotates 360∘ in 12hr or 720 minutes

So in x minute the hour hand will increase the reflex angle by 360x720=(x/2)^∘

In this x minute the minute hand will decrease the reflex angle by (6x)^∘ .

Hence

210^∘+(x/2)^∘−(6x)^∘=180^∘

⇒x=(60/11) minute

So at 7 past 55/11minute the hands will become opposite to each other.