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CLOCKS (ANGLE)

ANGLES


A clock is composed of 360 ° with 12 equal divisions. (i.e. 60 Minutes)

The angle between any two consecutive divisions = (360°)/12= 30° or 1 Min = 6 °A

Angular value of a minute = (30°)/5= 6°

Speed of the hands

Each needle of a clock covers the angle of 30°  to go from one division to the next, but it takes different times to cover this distance.


  • Speed of a second hand = 360° per minute. 


  • Speed of a minute hand = 6° per minute.


  • Speed of an hour hand =1/2 ° per minute.



 Example :

Q 1. How much degree is covered by minute and hour hand between 02 :00 p.m. to 04 : 00 ?

  1. 120 ° and 180 °

  2. 60 ° and 120 °

  3. 120 ° and 60° 

  4. 60 ° and 720 °

Sol : Between 02: 00 to 04 : 00 = 120 minutes.

Distance covered by Hour hand =   120 * ½ = 60 ° 

Minute hand = 120 * 6 ° = 720 ° = 2 rounds of the clock


Q 2.  How much degree is covered by  hour hand between 12 noon to 03 : 45 p.m. ?

  1. 112.5 °

  2. 150 °

  3. 90 °

  4. None of these

Sol :  Between 12: 00 to 03 : 45 = 3 hours + 45 minutes = 225 minutes

Distance covered by Hour hand = 225 * ½  = 112.5 °


Q 3. What is the angle between both the hands at 7 : 30 ?

  1. 30 °

  2. 44 °

  3. 315 °

  4. None of these

Sol : Between 7 Hour and 30 minutes = 45 °   

But option is not available, therefore, Angle between 7 Hour and 30 minutes = 360 ° - 45 ° = 315 °.

( Greater Angle )

Option C is the correct answer.

 

FOOD FOR THOUGHT : Both the hands means Minute and Hour hands (By Default)

 

Quickest Approach : 

To find the Angle =     60  H   -  11 M

                                     ━━━━━━

                                                 2

Here , H = Hours     ;  M =Minutes   ;     - = Difference


Q 4. What is the angle between both the hands at 5 : 10 ?

  1. 265 °

  2. 95 °

  3. 135 °

  4. Both A and C 

Sol :  60 * 5 - 11 * 10 

         ━━━━━━━    = 95 °

                     2

Or, Greater Angle =  360 ° - 95° = 265 °

Hence, the answer is 95 ° or 265 °.

So, the correct option is D


Q 5. What is the angle between both the hands at 5 : 40 ?

  1. 80°

  2. 240 °

  3. 290 °

  4. Can’t be Determined

Sol :  60 * 5 - 11 * 40                300 °- 440 °          

         ━━━━━━━    =     ━━━━━━━    =   70 ° 

                     2                                     2

Or,  Greater Angle =  360 ° - 70 ° = 290 °


Q 6. What is the angle between both the hands at 12 : 20 ?

  1. 120 °

  2. 110 °

  3. 100 °

  4. 130 °

Sol : Consider 12 : 20 = 00 : 20              { Just to ease the Calculation }

          60 * 0 - 11 * 20              220 °          

         ━━━━━━━    =     ━━━    =   110 ° 

                     2                              2

Or ,Greater Angle =  360 ° - 110 ° = 250 °


Q 7.  What is the angle between both the hands at 7 : 46   4/11 ?

  1. 45 ° 

  2. 325 ° 

  3. 55 ° 

  4. 305 ° 

Sol : 7 : 46  4/11 can also be 7 : 510/11

           60 * 7 - 11 * 510 / 11             420° - 510 °           

         ━━━━━━━━━━     =     ━━━━━   =   45 ° 

                     2                                               2

Or, Greater Angle =  360 ° - 45 ° = 315 °


Q 8. What is the angle between the hands at 2 : 00 ?

  1. 120 ° 

  2. 220 ° 

  3. 180 ° 

  4. 60 ° 

Sol :  Angle between the hands at 2 : 00 =  30 * 2 = 60 °  

SHORT TRICK: Since the value of minute hand becomes Zero, Multiplies the value of hours by 30 only.


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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