Aptitude - Clock - Discussion

The minute hand moves 360 degrees in 60 minutes. This means that the angle of the minute hand is given by 6t, where t is number of minutes past midnight.

The hour hand moves 30 degrees in 60 minutes. This means that the angle of the minutes hand is given by 0.5t.

The hands start together at midnight. The first time they make a 180 degree angle is when the minute hand has moved 180 degrees further than the hour hand, so this is given by the equation:

6t = 0.5t + 180
5.5t = 180
t = 360/11

So, after every t minutes there will an angle of either 180 degrees or 0 degrees alternatively.

24 hours is 1440 minutes.
1440 / (360/11) = 44.

Out of 44 times, at 22 times angle between minute hand and hour hand will be 180 degrees.

Method to solve it.

If we consider hour hand to increnment after 12 minute hand.

Then,

HH at 12:00 for MH between 12:00 to 12:11, but will be opposite directions if HM-12:00 & MM-&6:00, so condition is not satisfied.

Similarly if we calculate for 12:01, 12:02, 12:03, 12:04, 1:05, 1:06, 1:07, 1:08, 1:09, 2:10, 2:11, . So on. Till 11:59. Condition will satisfy only for 12:32, 1:38, 2:43, 4:54, 5:59, 6:00, 7:05, 8:10, 9:16, 10:21, 11:27.

11 times. Multiplied by 2 (for both a. M and p. M) =22.

Hence answer is 22.

I want to ask something that at 5:59 and 6:00 o'clock the hour hand and minute hand of the clock will be in opposite direction.

If you want to check you can practically check so the answaer will be 24.

If Answer Is This ( The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).) So
(The hands of a clock point in opposite directions (in the same straight line)(Because between 1 and 11 they point in opposite directions at 6 o'clcok only).

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.

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....:)

@Dhanancheziayn.

But from 12 to 1'o clock two hands will be in opposite directions once.

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

Assume we start with both hands at 12.

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

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