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.