Aptitude - Clock - Discussion

Hi guys it simple only, just take 1 time piece and try it yourself.

The hand of the clock point in opposite direction 11 times in every 12 hours ...for every 1 hr the min hand and hour hand are in the opposite direction i.e they are in the same straight line but at the time 5 both the hands are not meet the straight line at 6 o clock only it will met the opposite direction so only they said 11 times in 24 hours ... hope u understand.

When minute hands complete full circle in every hour, then how can it be possible that both hands are not in straight line and opposite direction?

This hapns evry 65 min(approx)for each case
=>in 1 day 24 hrs=> 24x60 min

Therefore each case hapns (24x60)/65 times each day................= 22(approx)

Therefore total # of times = 22+ 22=44

For 1 hr Minutes hand moves 60 mins and Hours hand(HH) only 5mins

it means to say Minutes Hans(MH) gains 55 mins over HH.

But be opposite the minutes hand should be 30 mins apart from HH.

55 mins of MH gained in 60 mins
1min gained in 60/55 mins
So 30 mins gained in (60/55)*30
So in 1 hr MH gains (360*2)/11

So in 24 hrs is (24*60)/(720/11)=22 times .

Just turn the hands of the clock. You'll come to know.

Assume we start with both hands at 12.

the event occurs after every (2*n +1)*6/11 hours....where n=0,1,2....

in 1 hour ,hour hand covers 30 degrees.

So in X hours and M minutes hour hand will cover (30X+M/2) degrees.

Now at the same time minute hand will cover 6M angle in M minutes.

So angle between hour hand and minute hand should be
(5.5M-30X) and this difference should be 180 degrees

Now when X=0 at midnight we get M as 32.73 minutes
and when X=1 ,M=38.19

Now differnce 38.19-32.73=5.46 minutes

So during 12 hrs 65.52 minutes i.e. 1 hr is lost

So thats hour hand n min hand comes in a line for 11 times in 12 hrs and 22 times in 24 hrs

Take a watch rotate check it.

Well this is very simple....some here want formula or logic.....but i can suggest you a logic.
well in question number 11 ....in discuss forum...some one has used da logic..
6t=0.5t+ 90 (if it is 90degree) ...check it out..
i will use the above concept
..
..
assume both hour hand and minute hand are at 12..means 12 o clock..
..
when they will be at 180 degree??
ans:6t =0.5t + 180
5.5t=180
t=360/11.
=32*8/11
it means they will be at 180 degree at 12:32 something...

{u can also use the formula
theta= 30h - 11/2*m
put theta=180,h=12,find m....you will get da same answer
}

now the question is when they will be at 180 degree.....just try to visualise (your mind will strike dat arnd 1:35 they will be at 180 degree)...

so 6t =0.5t + 540
5.5t = 540
t=1080/11
=98*2/11
i.e at arnd 1:38....

(why 540??? ) ans:1st we took 180.....then for again to be at 180 degree..i.e in da next hour....it has to rotate 360 more so dat they can be in opposite direction...
so 360 + 180=540......here we are taking 12 o clock as reference...

so 1080/11 -360/11= 720/11=65*5/11..
so for every 720/11(or 65*5/11) they are in opposite direction..

in a day total 1440 min..
number of times they will be in opposite direction is
1440/(720/11)=22...
i hope every1 got it....:)

NO. the answer is 24. If you count the number of hrs in a day i.e. 24. Therefore use to a clock to count it. Its 24 times starting from 12:00 am to 12:00 am again of next day. Thus the answer is 24.