Aptitude - Clock - Discussion

Discussion :: Clock - General Questions (Q.No.15)


At what time between 9 and 10 o'clock will the hands of a watch be together?

[A]. 45 min. past 9
[B]. 50 min. past 9
49 1 min. past 9
48 2 min. past 9

Answer: Option C


To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in 60 x 45 min or 49 1 min.
55 11

The hands are together at 49 1 min. past 9.

Sakshi said: (Oct 22, 2010)  
How do we know that min? Hand has to gain 45 mins?

Yamini said: (Dec 6, 2010)  
Why you take the 55 min spaces ?

Krish said: (Dec 12, 2010)  

The question is between 9 and 10 both the hands must coincide,.

So for the minute hand to reach 9 it has to gain 45 minute spaces.

Vipin said: (Jan 15, 2011)  
Alternative method::

Let the minutes covered when d situation occurs = x
(total degrees covered by minute hand) - (total degrees covered by hr hand)= (outer angle between 12 and 9) i.e.
6x - x/2 = 270

x=540/11 which is our ans. :)

Manish said: (Feb 5, 2011)  
I don't understand this method please explain it. Why we take 55 min ?

Shree Hema said: (Feb 13, 2011)  
better use this formula
if both hands coincide degree ll be 0
if both hands r in opposite direction degree will be 180
if both hands r in right angle degree will be 90
here it coincides so 0 degree
we have to find min only so keep that parameter(m) as it is, use minimum hour for hour parameter(h=9)
m=49 1/11
Got It???

Krishnadas said: (Jul 10, 2011)  
@sree. Good work. But is this formula standard?

Avijeetkumar said: (Aug 12, 2011)  
@shree. You are right.

Senthamizh said: (Aug 12, 2011)  
@Shree: is that standard formula???

Anil said: (Oct 29, 2011)  
If time is between x and y:

[x*5+angle]*(12/11) past x.

Pradeep said: (Dec 9, 2011)  
Here we can use the formula:
same direction means 0 degree; hour=9
m=49 1/11

Jasraj Khatri said: (Dec 19, 2011)  
When minute hand reach to 9, hour hand reach near to 10. Then why you count 45 spaces?

Kapil said: (Dec 25, 2011)  
It's very simple..

in 12 hour a hour hand gains angle= 360 degree
so in one hour it will gain = 360/12 = 30 degree


in 60 minutes a minute hand gains = 360 degree
so in 1 minute it will gain = 360/60= 6 degree

so angle gain by hour hand at any time = 30*[y+(x/60)] degree
& angle gain by minute hand=6*x degree

where y=no. of hour (in this question it is '9')
x=minutes after the y O' clock..

angle gained by hour hand should be Equuleus to minute hand..

=> 30*[9+(x/60)]=x*6
=> 270+ x/2=6x
=> 540+ x=12x
=> 11x= 540
=> x= 49 1/11

Nivesh said: (Feb 9, 2012)  
Thanks Kapil you have explained it in a very basic manner.

$Hr!Dhar said: (Aug 26, 2012)  
@Shree Hema: Hats Off To u!!! Awsm Formula!!
thnks ;)

can u plz give derivation of formula...

Goku said: (Nov 8, 2012)  
Keep it simple friends! Just use this formula.

12/11 (minutes to be gained). See in the question between 9 to 10'o clock we know that at 9:45 the hands will coincide so 45 minutes is to be gained from 9 o'clock.

So 12/11* (45) =49 1/9 (Answer).

Gaurav Mittal said: (Dec 10, 2012)  

We know that the hour and the minute hand will coincide somewhere between 9 and 10. At 9:45, the angle between the hour & the minute hand is 22.5 degrees (the hour hand gains 0.5 degree per minute, i.e. 45/2 degrees in 45 mins).

Now, assume that the minute and the hour hand coincide at x mins after 9:45.

So, in x mins, the hour hand moves x/2 degrees while the minute hand moves 6x degrees.

So, 6x - x/2 = 22.5 (i.e. from the original position to the new position)

So, x = 45/11 = 4 1/11.

So, the time at their meeting is 49 1/11.

Niki said: (Jul 12, 2013)  
@Gaurav Mittal.

How you counted moves for minute hand ? i.e. You took 6x. How? Can you please explain?

Inoo said: (Nov 5, 2013)  
What does this means 55 min. spaces gained in 60 min ? what does spaces here means?

V.K said: (Nov 29, 2013)  
Total distance the minute hand cover with respect to hour hand is 270'

And the relative speed is 5.5.

So the time to cover is,

270/5.5 = 540/11.

Rossy said: (Mar 7, 2014)  
Can someone please explain me, what is the main concept used to solve this problem?

Niraj Kumar said: (Aug 15, 2014)  
When the hands of watch together at that time it is obvious that angle made by hour's hand = angle made by minute's hand.

Let us assume both hand meet at time (9+x/60), where x = minute.

Now, (9+x/60)*360/12=x*360/60 (angle made by both hand).

After solving this equation, we find x=540/11. So ans=9hr, 540/11min. i.e = Option C.

Chandresh said: (Sep 16, 2014)  
You can try this way also.

360 = 30(10)-(11/2)m.
360-300 = (11/2)m.
(60*2)/11 = m.
m = 120/11;

Now just do: 60-(120/11) = 540/11 = 49.1/11.

A K Singh said: (Jan 7, 2015)  
What master formula you are giving its not applicable to a single question we are doing. All the time its having negative sign error. I don't think so that is the master formula but can say this is confusing the whole concept we read till now.

Jeet said: (Apr 15, 2015)  
In Q6 at 7, they are 25 mins apart, but in this Q at 9 they are 45 mins apart, is the angle measured clockwise/ anti clockwise?

Aarthi said: (May 12, 2015)  
Can you tell me the correct explanation?

Abhishek said: (Jul 13, 2015)  

Awesome man done in the most basic way manner as possible. Really appreciate your work.

Smita said: (Aug 4, 2015)  
Past 9n means?

Sonam said: (Aug 29, 2015)  
When asking will the hands of a watch be together?

Use (60/11)h.

= 60*9/11.
= 540/11.
= 49 1/11.

Bhavesh Kirange said: (Nov 18, 2015)  
I don't understand the concept here you are assuming. In question from 9 to 10 o'clock the hands should be meet each other on 9.50 o'clock in real situation by watch.

But how could you say here they are meeting on 9.45 o'clock means we are suppose to assume hour hand at stable position?

Rohan said: (Nov 27, 2015)  
Let QH and QM be angular speed of hour and minute hand respectively.

QH = 360/720 = 0.5 (degree/minute) QM = 360/60 = 6 (degree/minute).

Relative angular speed (QM-QH) = 11/2 = 5.5.

Now at 9:45 angle between minute and hour hand will be = 22.5 deg.

Time taken for minute hand to coincide hour hand = 22.5/5.5 = 45/11.

= 45/11 = 4+1/11.

Hence time at which hour and minute hand coincide is:

Hour = 9 minute = 45+4+1/11 = 49+1/11 or 45 1/11 past 9.

Sree said: (Nov 29, 2015)  
Can any one say how we can say that 49 1/11 = past 9?

Laxmi said: (Jan 23, 2016)  
Hello guys.

In previous question one member said that for angle formula.

Less 6 clock use formula theta = 11/2*M-(30*H).

And above 6 clock use formula theta = (30*H)-11/2*M.

This question this above 6.

But @Pradeep use formula is less 6.

I totally confused which one is correct formula in this question.

And when we use angle both the formulas. Any one please explain.

Sank said: (Mar 10, 2016)  
We can solve this question as a speed - time question.

Initially at 9'o clock hour hand will be at 9 and minute hand will be at 12.

In 12 hour a hour hand gains angle = 360 degree.

So speed of hour hand will be 0.5 deg/min.

In 60 minutes a minute hand gains = 360 degree.

So speed of hour hand will be 6 deg/min.

Let after hour hand covers angle x both the hands coincide.

So angle covered by hour hand = x and by minute hand = 270+x.

x/0.5= (270+x)/6 (as time taken by both will be same).

x = 270/11.

As 1 min = 6 degrees, so we can convert above angle(x) in degree to minute.

So in minute it will be (270/11)/6 = 45/11.

So the time when both of the clock hands will coincide is 49 1/11.

Rohit@ said: (Mar 28, 2016)  
I think it has gained 50 min space.

Akhilesh said: (Apr 23, 2016)  
My solution is:

Both the hands will meet somewhere between 9 and 10 i.e after the minute hand has reached 9 ( after 45 minutes). In these 45 mins the hour hand must also have traveled forward by some angle.

The angles covered by the hour hand in 45 mins will be 22.5. (how? in one min it covers 1/2 that's why!).

Now, let's suppose it takes another x mins for both of them to reach the point where they will coincide.
The angle traveled by hour hand will be x/2 and by the minute hand will be 6x.

Now in order to coincide with the hour hand, the minute hand has to cover the total angle the hour hand has moved forward.

So, 6x = x/2 + 22.5.

Ramya said: (Dec 29, 2016)  
I can't understand please explain it.

Rakha said: (Mar 21, 2017)  
What to do when you take minute spaces in degrees instead of minutes?

Babita Dogra said: (May 7, 2017)  
How you take 55 mint? How it will come?
Explain it.!

Vinayak said: (Jul 26, 2018)  
How does 60/55*45 become 49 1/11?

Please if anybody can explain this?

Irfan Qureshi said: (Aug 9, 2018)  
Formula : (11/2)M - 30*H = 0.

We have to find min so put H and get M.

put the value and get the answer in Min.

Harshitha said: (Dec 26, 2018)  
How come past 9 minutes? please explain it.

Nisha Lakshmi said: (Mar 12, 2019)  
BTW 9 and 10 the hand of the clock will be together at 9:45(min and hr hand coincides).
Since 55 min gained by min hand in 60 min.
Thus 1 min gained by min hand in 60/55 min.
Now 45 min gained by min hand in 60/55 * 45 = 540/11 min.

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