Aptitude - Clock - Discussion

@ALL.

I AM NEW TO THIS COMMUNITY,
NOW I WANT TO SHARE ABOUT CLOCK,
BEFORE GOING TO ATTEMPT ANY CLOCK PROBLEMS,
1.HOUR'S HAND TAKES.
=============HOURS HAND/ SHORT HAND=============
Time to finish one cycle = 360's.
i.e in 12hrs of time =360 degrees.
Within 1 hour of time = 360/12 =30 degrees.
Which means 60 mins = 30 degrees.
In one minute = 1/2 degree (half degree).
=============MINUTES HAND/ LONG HAND=============
Within 1 hour of time =360 degrees.
Which means 60 mins = 360 degrees.
In one minute = 360/60 = 6 degrees.

I think this stuff will help to solve any clock problem.

Why we multiple it by 31/6?

5:10 = 5+(10/60) = 5+1/6 = 31/6 hrs.

1 hr = 30 degrees,

31/6 hrs = 31/6 * 30 = 155 degrees.

Firstly, convert 5hrin minutes.
5*60=300
Add 10 min
=310min.

Now convert 310min in hr.

310min=310/60=31/6hr.
1 hr=(360/12)°.
31/6hr=(360/12)*31/6=155°.

1 hour it takes 30 degree, 5:10, 5*30=150, 1 miniute =1/2.

10 miniutes =5, total =150=5=150.

(30*hr+11/2*min)-360.
(30*5+11/2*10)-360=155.

5 hours + 10 minutes.

5*30°+ 10*0.5° {Angle made by hour hand in 1 hour =30°, the angle made by hour hand in 1 min=0.5°}
150°+5°
155°.

Hour hand completed 150 (90+60) upto 5 o'clock.

Now, for more 10 minutes past hour hand will move 5° (30° in 60 minutes multiplied by 10 (i.e. 1/2 degree per minute).

Hence total movement 150+5=155.

10 min past to 5 means time is 4:50.

1hr=30degrees.

Therefore 5hr and 10min=5*30=150=X.
=10min=5degree=Y,
Z=X+Y,
Z=150+5,
Z=155 degree.