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CLOCKS (TIME)

  Problems Based on Time


Time = 2 / 11 (A₁ +/- A₂ )

                   Here,  A₂ = Given Angle

                     A ₁ = Smaller Number * 30 

The value of time is  ( in minutes ) and must lie between 0 and 60. 

Therefore,    0   greater than   2 /11 * (A₁ +/- A₂ )  less than   60                


FOOD FOR THOUGHT : 

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

  • Any angle forms twice between the duration of 1 hour. 

  •  Once the angle forms before the coinciding of the Minute and Hour hand .

  • Second time , it forms after the coinciding of the Minute and Hour Hand .

  • Exception, some angle forms twice after the coinciding while sometimes it forms before coinciding. 

 

Q 1. At what time between 7 and  8 O’clock are the hands at an angle of 45 ° ?

Sol : Here A₁ = 7 * 30 = 210 °    and  A₂ = 45 °

       Time = 2 / 11 ( 210 +/- 45 ) 

    Case 1 : While Adding                       Case 2 :  While Subtraction 

     Time = 2 / 11 ( 210 +45 )                        Time = 2 / 11 ( 210 -45 ) 

              = 2 /11 ( 255 )                                           =  2 / 11 ( 165 ) 

              = 510 / 11                                                     =  2 * 15

              = 46 4 /11                                                  = 30 


Hence,  the answer is at 7 : 30 and at  7 : 46 4 /11  , the angles are at 45 ° between 7 and 8 O’clock . 


Q 2. At what time for the first time between 5 O’clock and  6 O’clock are the hands at an angle of 95 ° ?

Sol : Here A₁ = 5 * 30 = 150 °    and  A₂ = 95 °

        Time = 2/11 (150 +/- 95 )

Case 1 : While Subtracting      

     Time =  2/11 * ( 150 -95 )   

              = 2/ 11 * ( 55 )                      

              = 2 * 5       

              = 10   

Hence,  at 5 : 10  there is an  angle of  95 ° between  5 O’clock and  6 O’clock .


Q 3. At what time between 5 : 30  and  6 O’clock are the hands at an angle of 70 ° ?

Sol : Here A₁ = 5 * 30 = 150 °    and  A₂ = 70 °

Case 1 : While Addition      

     Time =  2/11 * ( 150 + 70 )   

              = 2/ 11 * ( 220 )                      

              =     2 * 20       

              = 40             

Here, we only have to do the Addition because we need to calculate the value after 5 : 30.

If we calculate the value by subtraction, the value obtained is less than 5 : 30. 


Q 4. At what time between 3 O’clock and  4 O’clock  is the minute hand 7 minute away from the hour hand ? 

Sol : Speed of minute hand is 6° / minute .

 According to the question, the minute hand is 7 minutes away from the hour hand. 

Therefore, For & minute = 7 * 6° = 42 ° .

The desired angle is 42 ° . 

So, Here A₁ = 3 * 30 = 90 °    and  A₂ = 42 °

 While Addition      

     Time =  2/11 * ( 90 + 42 )   

              = 2/ 11 * ( 132 )                      

              =  2 *  12

              = 24  

At 3 : 24 , the minute hand is 7 minute away from the hour hand.     


Q 5. At what time between 3 o'clock and 4 o'clock is the minute hand 4 minutes behind the hour hand?

Sol : Speed of minute hand is 6° / minute .

 According to the question, the minute hand is 4 minutes away from the hour hand. 

Therefore, For & minute = 4 * 6° = 24 ° .

The desired angle is 42 ° . 

So, Here A₁ = 3 * 30 = 90      and  A₂ = 24 °

 While Addition      

     Time =  2/11 * ( 90 - 24 )   

              = 2/ 11 * ( 66 )                      

              =  2 *  6

              = 12  

At 3 : 12 , the minute hand is 4 minute away from the hour hand.


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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