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

2 Answers

7:60/11 \text{pm}7:6011pm

Explanation:

The minute & hour hands of a clock will be opposite to each other i.e. angle between hands will be \theta=180^\circθ=180 after x=7x=7:00 pm past yy minutes given as follows

y=(5x-\theta/6)\times 12/11y=(5xθ6)×1211

=(5\times 7-180^\circ/6)\times 12/11=(5×71806)×1211

=60/11\ \text{minutes}

Jul 4, 2018

Just at 7.00pm the hour hand is at 7 and minute hand is at 12. Each minute division makes 6^@ at the center.

At 7.00pm 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 (360x)/720=(x/2)^@

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

Hence

210^@+(x/2)^@-(6x)^@=180^@

=>x=(60/11) minute

So at 7 past 5 5/11minute the hands will become opposite to each other.