Aptitude - Clock - Discussion

How you take 55 mint? How it will come?
Explain it.!

Formula : (11/2)M - 30*H = 0.

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

M=min.
H=Hour.
put the value and get the answer in Min.

How come past 9 minutes? please explain it.

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.

θ angle gained from by hrs clock at the time of meet from the past 9.
θ= [(45+M)/60] *30 30 degree for each hour.
θ = M/5 *30 30 degree Minutes hand move every 5 min.
So, equate them you'll have.
M= 45/11.
So meet time will be 45+M;

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

similarly,

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

Why you take the 55 min spaces ?

Sakshi,

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.

Alternative method::

Let the minutes covered when d situation occurs = x
now,
(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. :)

I don't understand this method please explain it. Why we take 55 min ?