Aptitude - Clock - Discussion

Discussion :: Clock - General Questions (Q.No.14)

14. 

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

[A]. 45 min. past 4
[B]. 40 min. past 4
[C].
50 4 min. past 4
11
[D].
54 6 min. past 4
11

Answer: Option D

Explanation:

At 4 o'clock, the hands of the watch are 20 min. spaces apart.

To be in opposite directions, they must be 30 min. spaces apart.

Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

50 min. spaces are gained in 60 x 50 min. or 54 6 min.
55 11

Required time = 54 6 min. past 4.
11


Aravind said: (Nov 27, 2010)  
If any tell me how is it come 30 min space apart...

Siri said: (Dec 27, 2010)  
I am not clear above answer any one tell me.

Srikanth said: (Jan 4, 2011)  
Here 30 min space apart means for opposite directions of minute hand and hour hand 30 min space apart.

Shree Hema said: (Feb 13, 2011)  
Here we can use the formula:
theta=11(m)/2-30(h)
opposite direction means 180 degree; hour=4
180=11(m)/2-30(4)
m=54 6/11

Shivakarthik said: (Feb 23, 2011)  
Its simple only so i think formula s no need for this ... if both the hands r in opposite direction or in the same straight line in 30 mins spaces ... v have 2 find out the time b\w 4 to 5 . at the time of 4 the spaces b\w the both hand s 20 min so 20=30=50 ...
60/55*50 =54*6/11min past4. hope u will understand?

Shivakarthik said: (Feb 23, 2011)  
Its simple only so i think formula s no need for this ... if both the hands r in opposite direction or in the same straight line in 30 mins spaces ... v have 2 find out the time b\w 4 to 5 . at the time of 4 the spaces b\w the both hand s 20 min so 20+30=50 ...

60/55*50 =54*6/11min past4. hope u will understand?

Neeraj said: (Jun 5, 2011)  
Why 50 min why not 10 min to be 30 spaces apart ?

Xyz said: (Aug 3, 2011)  
@Neeraj

Because the minutes hand can move only in clock-wise direction. So 20 min to reach at the same place as the hour hand + 30 min reach in the opposite direction.

Xyz said: (Aug 3, 2011)  
Can somebody tell me why it will gain only 55 min spaces in 60 min?

Abc said: (Aug 7, 2011)  
Same query as xyz have. Please answer it if any one knows.

Aravind said: (Aug 11, 2011)  
@xyz can you explain that 20+30 again?

Ranjit said: (Sep 2, 2011)  
Assume that they are in opposite directions after x mins..
Then minute hand has traveled x mins...
The hour hand has traveled (x*5)/60 mins from the 4 o' clock position. To this add 20 min to give (x/12)+20 min as its displacement from 12 o' clock...
Now the difference between their positions is 30 mins..
So solve x-((x/12)+20)=30.

Tunu Agrawal said: (Sep 22, 2011)  
Minute hand will have to gain 50 min. Spaces. From where did it come?

I m unable to understand it.

Upendra said: (Nov 16, 2011)  
It clearly shows that,
2 hands between 4 and 5'O clock means........
time is 4hours 54 mins
Now plz give explanation ..........

Pasumarthy said: (Nov 22, 2011)  
@xyz, @abc let's say initially both are at 12, after 60 min hours is at 1 and minutes hand at 12. So, in 60 min they traveled 55 min spaces apart.

Varun said: (Jan 18, 2012)  
At 4 o clock the hands are 20 minute apart.
to be just at opposite i.e at 180 degree opposite. the minute hand must travel 20+30 minute = 50 minute i.e at around 4:50.
thus in 50 minute minute hand travels= 50*6 degree= 300 degree
thus time taken to travel this distance= 300/(11/2)= 600/2 minute

Bhojraj said: (Feb 3, 2012)  
At what time between 5 'o' clock and 6 'o' clock, the hands of a clock will be 3 minutes apart.

Ajit said: (Jun 14, 2012)  
Where the 55 min comes from ?

Suresh said: (Oct 12, 2012)  
angle =11/2Min-30*Hours
so,180=11/2Min-30*4
180+120=11/2Min
min=300*2/11
Min=600/11

Nithya said: (Jul 30, 2013)  
Where the 55 minutes comes from?

Blcklstd said: (Aug 24, 2013)  
@Nithya 55 min gained in 60 minutes means.

Suppose its 12:00 am (both the hands of clock have 0 min. difference between them,as they both point towards 12 )then after 60 min(1 hour) hour hand will point to 1, and minute hand will point to 12, now in this position minute hand and hour hand have a difference of 55 minutes between them.

Thats wat he is telling that minute hand gained 55 min in 60 min.

Adafish said: (Aug 27, 2013)  
Is there any formula if the hands are apart my minutes?

Say eg., at what time between 5 and 6 o'clock the hands are 3 minutes apart?

Sikkanthar said: (Aug 28, 2013)  
Hi @Nithya and @Ajit.

"At 4 o'clock, the hands of the watch are 20 min. Spaces apart.

To be in opposite directions, they must be 30 min. Spaces apart.

Minute hand will have to gain 50 min. Spaces".

Are you agree this statement? the same thing "to reach the 5 o'clock in the opposite direction, they must be 30mins. Space apart.

Minute hand will have to gain 55min. Spaces.

(1-2-3-...11) => (5+10+... 55).

So the answer is (60/55) *50 = 54.(6/11).

V.K said: (Nov 29, 2013)  
Hi guy its very easy.

First of all at. 4 o' clock there is 120' space apart HM hand.

And for opposite direction there must be 180' space apart so,

Total is 300 space apart and the relative speed is 5.5 and the distance to Cover is 300. So, 300/5.5.

Kiranmai said: (Dec 29, 2013)  
Hi frnds here this can be solve in another way also:

((5*hour)-30)(12/11) because it is straight line.

((5*4)-30)(12/11).

(-10)(12/11).

(50)(12/11).

54.(6/11).

Nutan said: (Mar 24, 2014)  
How it 20 min spaces comes?

Kiran said: (Aug 23, 2014)  
-> Imagine if both the hands are 12 i.e time is 12:00 then at 1:00 -> Hour hand will be at 1:00 .

-> Minute hand will be at 12 again.Therefore the space gained by minute hand over hour hand is 55 min in 1 hour,i.e. 55 min in 60 min i.e logical data which is used in all problems.

-> Coming to the problem,the hour hand is at 4:00 and minute hand is at 12,therefore to cross hour hand the minute hand has to gain 20 min spaces i.e it means it has to move 20 min forward.

-> Between 4:00 and 5:00 if the hour hand and minute have to be in opposite directions,then hour hand will be at 5:00 and minute hand will be 55 then it has gain 30 minutes more.

-> Totally it has to gain 20+30=50 minutes.

-> If 55->60 then 50->? Ans = 54 6/11 min past 4 they will be in opposite directions.

Sachin Pachauri said: (Sep 22, 2014)  
Angle = 11min/2-30hour.
4 opposite direction angle is 180.

Between 4 and 5 o clock hour is 4.
You will get the min.(answer).

TRICK OF THIS TYPE OF QUESTION.

Raju said: (Sep 1, 2015)  
How 4 past come after dividing?

Priyanka said: (Sep 9, 2015)  
If we solve by the method of angle difference between hour hand and minute hand, there has to be a difference of 180 degrees for the hands to be opposite.

So I applied this in the equation. If they align 180 degrees opposite to each other after 'x' minutes, then degrees traversed by hour hand will be x*6 and that of hour hand will be (10*4) + (0.5*x).

Taking the difference, the equation formed will be 6x-40-0.5x = 180. Solving this equation gives x=40. So answer should be 40 minutes pas 4.

Akhila said: (Oct 15, 2015)  
Please explain anyone how the answer is 54/12 from (60/55*50).

Jayesh said: (Oct 28, 2015)  
Hi all,

Can someone explain me how is come space 30 and 55 min?

Sree said: (Nov 29, 2015)  
54 6/11 min. past 4 how?

Parul Saxena said: (Dec 24, 2015)  
Why 30-20=10 is not considered as it is done in question number 6?

Vidur said: (Apr 17, 2016)  
Find the time between 5 and 6 o'clock when the two hands of the clock are 6 minutes spaces apart.

Can anyone help me to solve this?

Sowmi said: (Sep 15, 2016)  
At 5 O' clock, the minute hand is 25 min spaces behind the hour hand.

Case 1:

The minute hand is 6 min spaces behind of the hour hand.
In this case, the minute hand has to gain (25 - 6) = 19 minutes spaces,
55 min spaces are gained in 60 min, 19 min spaces are gained in [(19/55) * 60] = (20) 8/11 min.

Case 2 :

Minute hand is 6min spaces ahead of the hour hand
In this case, the minute hand has to gain (25 + 6) = 31 minutes spaces
55 min spaces are gained in 60 min, 31 min spaces are gained in [(31/55) * 60] = (33) 9/11 min.

Tejas said: (Oct 16, 2016)  
Its simple just crosscheck each option given, you will get the desired answer like,
for option A:

4:45
4 + 45/60 = 19/4.
360/12 * 19/4 = 285/2°.

And
360/60 * 45 = 270°.

Clearly,
285/2 - 270 = Not equal to 180° (exact opppsite angle) likewise crosscheck all options you will get option D as the right answer.
D:
4 + 600/11 * 1/60 = 54/11°.
360/12*54/11 = 1620/11°.
And
360/60 * 600/11 = 3600/11°.

Then,
3600/11 - 1620/11 = 180° (exact opposite angle).

Nitin said: (Dec 7, 2016)  
Use this formula that is Min=60/11 * (Hr+6)

If Hr 1 to 5 make addition
If Hr 6 to 12 make subtraction.

Like Q 4 to 5 clock in opposite directions case

Min = 60/11 * (4+6)
= 60/11 * 10
= 600/11
= 54 6/11. Min. Past.

Harsh said: (Jan 28, 2017)  
How its 55min?

Initially its 12:00am hour and min hand makes 0° after an hour i.e 1:00am hour hand travels 5 min and minute hand travels 60 min so difference between hour and min hand is 55 min.

Sainath said: (Mar 10, 2017)  
Use this formula:

(5n-30)*12/11 for n>6.
(5n+30)*12/11 for n<6.

Suman said: (Mar 30, 2017)  
As per my calculation, the correct answer will be 55.38 min.

Owen Wilson said: (Apr 26, 2017)  
What does it mean when it says "55 min. spaces are gained"?

Pratima said: (Jul 17, 2017)  
Between 4 and 5, the minute hand to move 20 min in right half of circle (watch) from the initial point that is 12 here.

And 30 minutes from 4 in another side to go in opposite direction. So total is 20+30=50.

Ajay Kumar said: (Aug 8, 2017)  
You explained very well. Thanks @Kiran.

Nikita Agrawal said: (Dec 7, 2017)  
Somebody, please tell me the degrees of every direction.

Ash said: (Jul 4, 2018)  
Guys when to use (4h-11/2 *m) and when to use (11/2*m-4h). Can anybody please explain this?

Avijit Samanta said: (Jan 1, 2019)  
Use this formula:

(5n+30)*12/11 if n<6.
(5n-30)*12/11 if n>6.

Rinju said: (Jan 3, 2019)  
The two hands of a clock will be opposite direction between H and ( H+1) O' clock at 60a/11 minutes past H' O clock.

Solve this problem by using this method,
'a' is opposite to H,
In this case, H is 4 and a is 10,
Then 60*10/11,
600/11= 54 6/11 past 4.

Nithisha said: (Feb 22, 2019)  
It's very simple.

As it was mentioned opposite(180°).
180° = (11/2*m)-30(hr),
180° = (11/2*m)-30(4),
m = 600/11,
m = 54.5454.

Arunkumar said: (Apr 27, 2019)  
Thanks @Nithisha.

Shivam Tiwari said: (Jun 30, 2019)  
At 4'O clock ---------> 20 mins spaces.

To be in the opposite direction, they must have 30 mins spaces.

So, clock follows the only clockwise direction that's why it has to gain 50 mins spaces apart to be in the opposite direction.

55 mins spaces ----------------> 60 mins.
50 mins spaces---------------> 60/55*50 = 54(6/11)min.

So, the answer is 54(6/11)min past 4.

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