Aptitude - Clock - Discussion

@All.

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

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

Please if anybody can explain this?

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.

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?

Can you tell me the correct explanation?

@Kapil.

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

Past 9n means?

When asking will the hands of a watch be together?

Use (60/11)h.

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

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?

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.