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CLOCKS ( SPECIAL ANGLES )

Special Angles (0 ° and 180 ° and 90 ° )


FOOD FOR THOUGHT : 0 ° and 180 ° are the two angles which don't  form at all between the duration of 1 Hour.

  1. For 0 ° : (i.e. between 11 ‘O Clock to 12 ‘O Clock and Between 12 ‘O Clock to 1 ‘O Clock ). During this duration, only one time both the Hands coincides  sharp at 12 ‘O Clock.

  2. For 180 °  : ((i.e. between 5 ‘O Clock to 16 ‘O Clock and Between 6 ‘O Clock to 7’ O Clock ). During this duration, only one time both the Hands are opposite to each other sharp at 6 ‘O Clock.


Q 1. How many times are the hands together in a day ?

Sol :  In Hour = 1 time.

          In 12 hours = 12 - 1 = 11 times

         Between 11 'O'Clock to 1 ‘ O'clock, the time duration is 2 Hours. But the hands  coincide at

one time only i.e. right  at 12 ‘ O Clock. Therefore,In 12 hours Duration Hands coincide 1 time

less  in the complete duration of 12 hours.

       

Similarly,   In 24 hours = 22 times Hands coincides. (Forms 0 ° angle )


Q2. How many times are the hands opposite each other in a day ?

Sol : In 1 hour = 1 time

         In 12 hours = 12 - 1 = 11 time

        Between 5 'O'Clock to 7 ‘ O'clock, the time duration is 2 Hours. But the hands are opposite to

each other  at one time only i.e. right  at  6‘ O Clock. Therefore,In 12 hours Duration Hands are

1 time less at 180 ° in the complete duration of 12 hours.

 Similarly,   In 24 hours = 22 times Hands coincides. (Forms 180 ° angle )


Q3. How many times are the hands be right angled in a day ?

Sol : In 1 hour = 2 times. 

        In 12 hours = 24 - 2 times = 22 times           (At 3 ‘O clock and 9 ‘ O clock , only 1 time right angle forms.  At sharp 3 ‘ O clock and 9’ O Clock only.)

        In 24 hours = 48 - 4 times = 44 times 


Q 4. How many times are the hands together from 10 am to 3 pm ?

Sol : No. of Hours from 10 am to 3 pm. = 5 hours

        No. of times coincide = 4 times                     (12 O’Clock is included)


Q 5.  How many times are the hands together from 5 : 30 pm to 9 : 30 pm ?

Sol :  No. of Hours from 5 : 30 pm to 9 : 30 pm. = 4 hours

         Between 5 to 6 pm. = the hands coincide before 5 : 30

         Between 9 to 10 pm. = the hands coincide after 9 : 30

         Hence we need to check the duration 6 pm to 9 pm  = 3 hours

         No. of times coincide = 3 times                     (12 O’Clock is not included)


Q 6. How many times are the hands opposite to each other  from 10 am to 4 pm ?

Sol :  No. of Hours from 10 : 00 am to 4 : 00 pm. = 6 hours

         No. of times opposite to each other = 6 times.          (Because 6 O’Clock is not included.)



Q 7. How many times are the hands opposite to each other  from 4 pm to 10 pm ?

Sol :  No. of Hours from 4 : 00 pm to 10 : 00 pm. = 6 hours

         No. of opposite to each other = 6 - 1 = 5 times.       (Because 6 O’Clock is included.)


Q 8. How many times do the hands coincide and  opposite to each other  from 11 am to 5 pm ?

Sol :  Coincide : No. of Hours from 11 : 00 am to 5 : 00 pm. = 6 hours

         No. of times coincide = 6 - 1 times                     (12 O’Clock is included)

         Opposite to each other :  No. of Hours from 11 : 00 am to 5 : 00 pm. = 6 hours

          No. of opposite to each other = 6  times.       (Because 6 O’Clock is not included.)


Q 9. How many times are the hands be in a straight line for Sunday 5 PM to Monday 7 PM ?

Sol : FOOD FOR THOUGHT : Straight line = 0 ° (coincide) and 180 ° (opposite to each other)                                       (Mistake committed by students in the exam frequently.)

No. of Hours from Sunday 5 PM to Monday 7 PM. = 24 hours + 2 hours

     HANDS COINCIDE  

 No. of Hours from Sunday 5 PM to Monday 5 PM = 24 hours = 22 times

       Between 5 PM to 7 PM = 2 hours = 2 times        (Because 12 O’Clock is not included.)

HANDS OPPOSITE TO EACH OTHER

No. of Hours from Sunday 5 PM to Monday 5 PM = 24 hours = 22 times

Between 5 PM to 7 PM = 2 hours = 1  time          (Because 6 O’Clock is included.)

No of times = (22 + 1 ) +( 22 + 2 ) = 24 + 23 = 47 times

       Hence the answer is 47 times hands be in a straight line. 


Q 10. How many times are the hands at right angles from 1 pm to 5 pm ?

 Sol : No. of Hours from 1 : 00 pm to 5 : 00 pm. = 4 hours

     No of times Right angle forms from 1 : 00 to 5 : 00 = 2 * 4 - 1 = 8 - 1 = 7 times. 

   (Because 3 PM is included in the duration)


Q 11. How many times are the hands coincide, opposite to each other and are  at right angles from 5 pm to 11 pm ?

Sol : No. of Hours from 5 : 00 pm to 11 : 00 pm. = 6 hours

No. of times Hands coincides = 6 times                            (Because 12 O’Clock is not included.)

No.of times Hands  Opposite to each other = 6 - 1 = 5 times    (Because 6 O’Clock is included.)

No of times Hands are at right angle = 2*6 - 1 = 12 - 1 = 11 times

  (Because 9 PM is included in the duration)

 

Q 12. How many times are the hands coincide, opposite to each other and are  at right angles from 2 pm to 10 pm ?

Sol : No. of Hours from 2 : 00 pm to 10 : 00 pm. = 8 hours

No. of times Hands coincides = 8 times                            (Because 12 O’Clock is not included.)

No.of times Hands  Opposite to each other = 8 - 1 = 7 times       (Because 6 O’Clock is included.)

No of times Hands are at right angle = 2*8 - 2 = 16 - 2 = 14 times  

(Because 3 PM and  9 PM is included in the duration)


Ask me in the comment section, if you face any problem while solving clock aptitude questions. Visit next page for more clock problems.


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