Aptitude - Clock - Discussion

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....:)

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.

In 60 min. 55 minute spaces are covered.

So lose of 5 min.

That is in 1 hour we lose 5 min.

So in 12 hour we will lose 12*5 = 60 min.

In 1 hour we will get only once when both the hands of watch will be in a straight line in opposite direction.

So we expect in 12 hour we should get 12 times both the hands be in a single straight line in opposite direction.

But unfortunately we have to minus the 1 hour that we have lost. That is one time we have to minus from 12 time.

That is in 12 hour we will have 12-1=11 time both the hand in straight line.

So finally in 24 hour we will get 22 times.

@Swetha

There is no need of formula , if you want formula for only this question then i don't think it is good. Instead of memorize any formula for this single question why don't you remember it's answer, it is much better, because if you calculate using formula it'll never give you different answer because it is universal truth.

Anyway I want to share if you aren't getting how it is calculated.

In every hour, once hour hand and minute hand will be in opposite direction. It means 24 times in a day, but due to loss of 2 hour, they'll be 22 times only simple.

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

No, its entirely wrong actually in 24 hrs hands will be in opposite direction only for 21 times i.e, on

12:30
1:38^2/11
2:43^7/11
3:46^1/11
4:54^6/11
6:00
7:5^5/11
8:10^10/11
9:16^1/11
10:54^6/11 & again
12:30 (by this 12 hrs are completed)
1:38^2/11
2:43^7/11
3:46^1/11
4:54^6/11
6:00
7:5^5/11
8:10^10/11
9:16^1/11
10:54^6/11 & again
12:30 (by this another 12 hrs are completed)

So, over all 24 hrs are completed and the hands will be in opposite direction in the above timings and only for 21 times not for 22 times.

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.

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.

The concept is we start from 12 they are one time opposite before 1 pm.

Similarly they will be opposite one more time before 2 pm. This is the condition till 5 pm but at 6 they are opposite at exactly 6 ( minute hand at 12 hour hand at 6 ) after this they will be opposite 7 times after 7 similarly opposite 11 times after 11 and 12 times after twelve gotcha after twelve so upto twelve only 11 times.

So in 24 hours 11+11 = 22 times.

It's not a straight line at 12:30. It's a straight line roughly around 12:33 because the hour hand will be halfway between 12 & 1 at 12:30. So 12-4 get 1 occurrence each. 5 does not get an occurrence as the hands won't line up perfectly until 6:00 sharp. 6 through 11 get 1 occurrence each. That means that in that 12-hour period, we get 11.

Repeat for the following 12 to get a 24-hr day.