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

2 Answers
Harish Chandra Rajpoot
Jul 4, 2018

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

Explanation:

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

#y=(5x-\theta/6)\times 12/11#

#=(5\times 7-180^\circ/6)\times 12/11#

#=60/11\ \text{minutes}#

P dilip_k
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 5/11#minute the hands will become opposite to each other.

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