Aptitude - Clock - Discussion

Discussion :: Clock - General Questions (Q.No.13)

13. 

How many times in a day, are the hands of a clock in straight line but opposite in direction?

[A]. 20
[B]. 22
[C]. 24
[D]. 48

Answer: Option B

Explanation:

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, in a day, the hands point in the opposite directions 22 times.


Bonny said: (Aug 17, 2010)  
I'm trying to find a formula for finding the hands of clock in straight line?

Swetha said: (Oct 3, 2010)  
Any formula derived?

Nitesh Nandwana said: (Oct 13, 2010)  
@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.

Dhanancheziayn said: (Dec 16, 2010)  
I'm still confusing in this............. can anyone reveals by doubt?

Somojit said: (Feb 13, 2011)  
In 12'o clock the two hands are on same direction, then why we are calculating it?

Karthik said: (Feb 23, 2011)  
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.

Himanshu said: (Apr 1, 2011)  
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?

Annirban Bhattacharya said: (May 2, 2011)  
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

Shahid said: (May 28, 2011)  
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 .

Narayanan said: (Jun 8, 2011)  
Just turn the hands of the clock. You'll come to know.

Rashmi said: (Jul 7, 2011)  
Assume we start with both hands at 12.

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

Kiran Nalawade said: (Jul 24, 2011)  
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

Navi said: (Jul 24, 2011)  
@Dhanancheziayn.

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

Anuragnayak said: (Sep 23, 2011)  
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....:)

Smit said: (Sep 27, 2011)  
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.

Ayaz Ali Bhacho said: (Nov 12, 2011)  
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).

Vimal said: (Mar 13, 2012)  
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.

Sunayana said: (Oct 14, 2012)  
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.

Rusted said: (Jun 22, 2013)  
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.

Kailash said: (Aug 17, 2013)  
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.

Electronics said: (Oct 7, 2013)  
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.

Mohan said: (Dec 10, 2013)  
The time between 5 and 6 o'clock when two hands of a clock are in same line making angle of 180 degree?

Akshaya said: (Aug 20, 2014)  
I have a doubt. You all say the hour and minute hands are in straight line only once between 5 and 7. What about 5:55?

Alka said: (Sep 27, 2014)  
Which angle a clock will make if both the needles are at 6.

Kishori said: (Jan 5, 2015)  
I want check. When in watch make time 2:45 pm that time which angle will be there.

Maddy said: (Jan 26, 2015)  
Take a watch rotate check it.

Rajneesh said: (Mar 11, 2015)  
Following are the time when they are straight.

12:30.
1:35.
2:40.
3:45.
4:50.
5:55.
6:00.
7:05.
8:10.
9:15.
10:20.
11:25.

And they are all 12.

Is I am missing something? How it is 11?

Garhwal said: (Apr 28, 2015)  
@Rajneesh.

The hands are not in a straight line at 5.55. Take a hand watch and see for yourself. This is the point being made. From 4:50, the next occurrence happens only at 6:00.

So in total, for every 12 hours, we have 11 such instances. For 24 hours, the number of instances is 11*2=24.

Sanchit Bhardwaj said: (Jun 18, 2015)  
Great this question was one of the mind buzzing.

And to tell you if you are taking opposite hands of watch as 12:30, 1:35 so on, then I am afraid your are wrong.

Because the hour hand won't be exactly on 12 if its 12:30, it will be at mid way of 12 and 1; and if its midway how can you put minute hand of watch on 12:30.

It should be somewhere around 12:32.5. Rest you can check manually.

Aman said: (Jul 28, 2015)  
I can't understand how there is the loss of two hours? Please tell me.

Vipul said: (Aug 20, 2015)  
See what you must be thinking there are 12 hours and you should get 12 opposite directions right in between every hour. 12-1, 1-2, 2-3, 3-4, 4-5. Now next moment will occur at 6pm (you can count it as between 5-6) , but next will occur at around 0705 that is 7-8, so there is no such thing between 6-7.

Amit said: (Sep 6, 2015)  
Answer is 22. Just try by yourself. Use a clock and start rotating its hands. You'll find your answer.

Rashpal Sin said: (Sep 19, 2015)  
7 clock in the opposite direction to rotate 180.

Similarly, the opposite direction of the clock 9 180 turned north end figure 3 to 6 are made. Please give me answer in detail.

Madhava said: (Jun 11, 2016)  
A watch, which gains uniformity was observed to be 6 minutes slow at 9 am on a Wednesday and 3 minutes fast at 12 noon on the subsequent Thursday. When did the watch show the correct time?

Solve and find the answer.

Anil Kumar said: (Nov 12, 2016)  
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.

Muhammad Azeem said: (Dec 16, 2016)  
@Anil Kumar.

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)

After 9:16, it is not at 10:54. it is at 10:21 and then 11:27.
So in total, 22 times.

Zoilo said: (Jan 14, 2017)  
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.

Tikeshwar Sahu said: (Feb 20, 2017)  
According to me,

Only 2 times in a day it happens mathematically. Actually, because for this there should be 180 degree difference between both hands and when hour hand travels 1 degree minute hand travels 12 degree so only 6 o clock it happens that actully difference between both hands is 180 degree. So answer is 2 times in a day.

Govorov said: (Mar 3, 2017)  
How many times the hour & minute hand are in opposite directions b/w 9PM & 10 PM?

Please answer it.

Ansh said: (Jun 8, 2017)  
Sir, how many times starting at 1pm would be the M and H hand make 40 degrees with each other in next 6 hrs?

Sohail said: (Jul 30, 2017)  
I don't know why its answer is 22. I think it should be 24.

Naveen said: (Aug 2, 2018)  
@Nitesh Nandwana,

What is that due to the loss of 2 hour?

Rahul said: (Sep 20, 2018)  
How many times needle overlap in a week in the clock?

Please answer it.

Post your comments here:

Name *:

Email   : (optional)

» Your comments will be displayed only after manual approval.