Solutions for Clocks

1.  30 H - (11/2)  M = 30(8)-(11/2)50

    =240-275=35⁰

2.  Difference in times i.e. 2.00pm – 9.00am =5hrs

      =5*30=150⁰

3.  Two hands coincide = 0⁰ angle between them

     Sum=minspace + required minspace < 60

     Time of coincidence =sum  ^sum/₁₁

      Required minspace=0 if 0⁰

     Minspace = x*5 where the time between x-y is considered

     Here x=6 so minspace =6*5=30

     Sum=30+0=30

     Time=30 ³⁰/₁₁   = 30 + (30/11) = 30 + (2 ⁸/₁₁) =32 ⁸/₁₁ =>6:32 ⁸/₁₁

4.  Two hands opposite =180⁰ angle between them

     Sum=minspace - Required minspace >60

     Time of coincidence =sum  ^sum/₁₁

     Required minspace=30 if 180⁰

     Minspace = x*5 where the time between x-y is considered

     Here x=9 so minspace =9*5=45

     Sum=45+30=75 > 60 so we will do 45 - 30 = 15

    Time=15 ¹⁵/₁₁   = 15 + (15/11) = 15 + (1 ⁴/₁₁) =16 ⁴/₁₁

5.  Two hands right angle = 90⁰ angle between them

     Sum=minspace + Required minspace

    Time of coincidence =sum  ^sum/₁₁

    Required minspace=15 if 90⁰

    Minspace = x*5 where the time between x-y is considered

    Here x=4 so minspace =4*5=20

    Sum=20+15=35 or 20-15=5

    Time=35 ³⁵/₁₁   = 35 + (35/11) = 35 + (3 ²/₁₁) =38 ²/₁₁ => 4: 38 ²/₁₁

     Or 5 ⁵/₁₁ => 4: 5 ⁵/₁₁

6.  Consider 11:60

      Now actual time is 9:45 so subtract it from 11:60 = 2:15 is its mirror time

7.  Note:-  Minute hand and hour hand meet every  65 5/11 min.

                  So the two hands  are coincide at 21 9/11 min past 4 .

8.  Two hands opposite =180⁰ angle between them

     Sum=minspace - Required minspace >60

    Time of coincidence =sum  ^sum/₁₁

     Required minspace=30 if 180⁰

     Minspace = x*5 where the time between x-y is considered

     Here x=7 so minspace =7*5=35

     Sum=35+30=65 > 60 so we will do 35 - 30 = 5

     Time= 5 ⁵/₁₁ => 7: 5 ⁵/₁₁ 

9.  Two hands right angle = 90⁰ angle between them

      Sum=minspace + Required minspace

      Time of coincidence =sum  ^sum/₁₁

      Required minspace=15 if 90⁰

      Minspace = x*5 where the time between x-y is considered

      Here x=6 so minspace =6*5=30

      Sum=30+15=45 or 30-15=15

      Time = 45⁴⁵/₁₁   = 45 + (45/11)
       = 45 + (4¹/₁₁) =49¹/₁₁ => 6: 49 ¹/₁₁

      Or 15 ¹⁵/₁₁   = 15 + (15/11) = 15 + (1 ⁴/₁₁) =16⁴/₁₁ => 6: 16 ⁴/₁₁

10.  Two hands coincide = 0⁰ angle between them

       Sum=minspace + required minspace < 60

       Time of coincidence =sum  ^sum/₁₁

       Required minspace=0 if 0⁰

       Minspace = x*5 where the time between x-y is considered

       Here x=9 so minspace =9*5=45

       Sum=45+0=45

       Time=45 ⁴⁵/₁₁   = 45 + (45/11)
        = 45 + (4 ¹/₁₁) =49 ¹/₁₁ =>9:49 ¹/₁₁