Clocks

CASE-1: Find an Angle between hands:      

 Angle between minute hand and hour hand of an clock in 1 minute= 6 degree

Angle between minute hand and hour hand of an clock in 60 minute i.e in 1hr= 360 degree

CASE-2:When hands will Coincide:

Initially at  time 00:00 minute hand and hour hand makes  0deg(zero degree) angle.and when minute hand completed 60minutes and hour hand completed only 5 minutes i.e in 60minutes i.e in 1hr minute hand is 55minutes (60-5=55) more than hr hand.so we can say that in 1hr minute hand gains 55minutes over hr hands.

If we want to find that when minute hand and hour hand will coincide each other between t1 and t2 time( we considering 12hrs  time format not 24hrs time format ).
where t1=1,2,3...11 and t2=t1+1

Then D=5*t1 minutes

Coinciding minutes CM= D*(12/11) minuts past t1

And hand will concide at D*(12/11) minuts past t1.

e.g1

Question: At what time between 2 and 3 o’clock will the hands of a clock be together?

Sol:

  here t1=2

so D=5*t1=5*2=10 minutes

Coinciding minutes=D*(12/11)minutes past t1

                                  =10*(12/11) minutes past 2

                                  = 10*(12/11)minutes past 2

e.g2

Question: At what time between 1:30 and 2:30 o’clock will the hands of a clock be together?

Sol:

We know that minute hand and hour hand will not meet  between 1:30 and     2 o’clock they will meet after 2 o’clock i.e between 2 and 3 o’clock the the question is same  as e.g1

CASE-3: when hands make a particular angle.

If we want to find that when minute hand and hour hand will make angle A between t1 and t2 time( we considering 12hrs  time format not 24hrs time format ).
t1=1,2,3...11 and t2=t1+1 

Then D=5*t1 minutes

           T1= D-(A/6)

           T2= D+(A/6)

    Angle making time AMT=T*(12/11)minutes past t1.

i.e  AMT1= T1*(12/11)minutes past t1

and AMT2= T2*(12/11) minutes past t1

e.g1

Question: At what time between 4 and 5 o’clock wil the hands of a clock be at right angle(i.e 90degree angle)?

Sol:

Here  t1=4,t2=5,A=90degree

          D=5*4=20

T1=D-(A/6)=20-(90/6)=5

And T2=D+(A/6)=20+(90/6)=35

So AMT1=T1*(12/11) minutes past t1

                =5*(12/11)minutes past 4

And AMT2 =T2*(12/11) minutes past t1

                =35*(12/11)minutes past 4

e.g2 

Question: At what time between 4:30 and 5:30 o’clock wil the hands of a clock be at right angle(i.e 90degree angle)?

sol:

 find the right angle between 4 and 5 'oclock and take a time of 4:30.then find right angle between 5 and 6o'clock  and take time before 5:30.