"Everything should be made as simple as possible, but not simpler."
- Albert Einstein
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 D
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.
I'm trying to find a formula for finding the hands of clock in straight line?
Swetha said:
(Sun, Oct 3, 2010 08:59:06 AM)
Any formula derived?
Nitesh Nandwana said:
(Wed, Oct 13, 2010 11:43:17 AM)
@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:
(Thu, Dec 16, 2010 07:01:21 AM)
I'm still confusing in this............. can anyone reveals by doubt?
Somojit said:
(Sun, Feb 13, 2011 02:55:24 PM)
In 12'o clock the two hands are on same direction, then why we are calculating it?
Karthik said:
(Wed, Feb 23, 2011 05:12:42 AM)
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:
(Fri, Apr 1, 2011 05:58:13 AM)
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:
(Mon, May 2, 2011 10:34:40 AM)
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:
(Sat, May 28, 2011 05:26:25 AM)
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:
(Wed, Jun 8, 2011 04:09:34 AM)
Just turn the hands of the clock. You'll come to know.
Rashmi said:
(Thu, Jul 7, 2011 03:12:41 AM)
Assume we start with both hands at 12.
the event occurs after every (2*n +1)*6/11 hours....where n=0,1,2....
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:
(Sun, Jul 24, 2011 07:07:18 PM)
@Dhanancheziayn.
But from 12 to 1'o clock two hands will be in opposite directions once.
Anuragnayak said:
(Fri, Sep 23, 2011 01:56:42 PM)
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:
(Tue, Sep 27, 2011 12:52:00 AM)
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:
(Sat, Nov 12, 2011 12:10:50 PM)
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).
