Aptitude - Clock - Discussion

Formula :
Θ = |11M/2 - 30H|.
0⁰=|11M/2 - 30*9|.
= 11M/2 - 270.
0⁰+270⁰=11M/2.
270*2/11=M.
540/11=M.
M = 49 1/11.

@All.

θ = (11m/2) - 30h is a standard formula.

55 = 60 min.
45 = x.
X= 60*45\55.
X = 540/11.
X = 49 1/11 past 9.

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.

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.

Thanks for explaining @Akhilesh.

How does 60/55*45 become 49 1/11?

Please if anybody can explain this?

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

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.