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CLOCKS (ERROR)


CLOCK (ERROR)

TYPE 1: When the Minute Hand overtakes the Hour Hand either fast or slow.

Example : If in a clock the minute hand overtakes the hour hand in 65 minutes of correct time then how much does the clock gain or loss in a day ?

a. 24/23 fast

b. 24/123 slow

c. 24/ 23 slow

d. 24/ 123 fast

Sol :                                5

           After every  65  ━━ minutes , Minute Hand overtakes the Hour Hand.

                                       11

According to question, the Minute Hand overtakes hour Hand in 65 minutes. The Clock is faster than the usual.

    We know that , 

                                     5

                              65  ━    ─ Given Time 

                                    11

                             ━━━━━━━━━━━ x Total Time

                                      Given Time

                                     5

                              65  ━    ─ 65

                                    11

                       =  ━━━━━━━━━━━ x 24 hours 

                                            65

                           

                                  5

                       =  ━━━━━ x 24 hours 

                              11 x 65

                               24

                       =   ━━━ hrs fast.

                              143


Example : If in a clock the minute hand overtakes the Hour hand in 60 minutes of correct time then how much does the clock gain or loss in 22 hours?

  1. 2 minutes

  2. 20 minutes

  3. 120 minutes

  4. 1200 minutes

Sol :  According to question, the Minute Hand overtakes hour Hand in 60 minutes. The Clock is faster than the usual.            

    We know that , 

                                     5

                              65  ━    ─ Given Time 

                                    11

                            ━━━━━━━━━━━ x Total Time

                                      Given Time

                                     5

                              65  ━    ─    60

                                    11

                       =  ━━━━━━━━━━━ x 22 hours 

                                            60

                                       5

                                  5 ━─

                                      11

                       =  ━━━━━ x 22 hours 

                                  60

                                60

                       =   ━━━━  x 22 hours

                              60 x 11

                      = 2 hours = 120 minutes Faster


Example : If in a clock the minute hand overtakes the hour hand in 70 minutes of correct time then how much does the clock gain or loss in 77 hours?

  1. 5 Hours Slow

  2. 5 Hours Fast

  3. 6 Hours Slow

  4. 6 Hours Fast

Sol : According to question, the Minute Hand overtakes hour Hand in 70 minutes. The Clock is slower than the usual.

We know that , 

                                     5

                              65  ━    ─ Given Time 

                                    11

                            ━━━━━━━━━━━ x Total Time

                                      Given Time

                                    5

                              65  ━    ─    70

                                    11

                       =  ━━━━━━━━━ x 77 hours 

                                            70

                                       6

                                  4 ━─

                                      11

                       =     ━━━━━ x 77 hours 

                                     70

                                50

                       =   ━━━━  x 77  hours

                              70 x 11

                      = 5 hours Slower


Type 2 : When clock is faster or slower by some minutes

Example : A clock which gains uniformly is 5 minutes slow on Sunday 5 PM if it is 7 minutes fast on Tuesday 5 PM then when was it correct ?

  1. Monday  8 AM

  2. Tuesday 8 AM

  3. Monday 1 PM

  4. Tuesday 1 PM

Sol : On Sunday 5 PM  → 5 Minutes Slow

         On Tuesday 5 PM → 7 Minutes Faster

        We know that 

                                 Slow /Fast time

                              ━━━━━━━━━ x Total Time 

                                Slow + Fast Time 

                       5

               =  ━━━ x 48 Hours                          [Sunday 5 PM to Tuesday 5 PM = 48 Hours]

                      12

               = 5 x 4 

               = 20 Hours.

           After 20 hours of Sunday 5 PM, Clock depicts Correct Time.

           Hence,   Sunday 5 PM + 20 Hours = Monday 1 PM


Example : A clock which gains uniformly is 8 minutes slow on Sunday 5 PM if it is 10 minutes fast on Wednesday  5 PM then when was it correct ?

  1. Monday  8 AM

  2. Tuesday 8 AM

  3. Monday 1 PM

  4. Tuesday 1 PM

Sol : On Sunday 5 PM  → 8 Minutes Slow

         On Wednesday 5 PM → 10 Minutes Faster

        We know that 

                                 Slow /Fast time

                              ━━━━━━━━━ x Total Time 

                                Slow + Fast Time 

                       8

               =  ━━━ x 72 Hours                       [Sunday 5 PM to Wednesday 5 PM = 72 Hours]

                      18

               = 8 x 4 

               = 32 Hours.

           After 32 hours of Sunday 5 PM, Clock depicts Correct Time.

           Hence,   Sunday 5 PM + 32 Hours = Tuesday 1 AM


Example : A clock which loss uniformly is 5 minutes fast on Sunday 5 PM if it is 7 minutes slow on Tuesday  5 PM then when was it correct ?

Sol : On Sunday 5 PM  → 5 Minutes Fast

         On Tuesday 5 PM → 7 Minutes Slow

         We know that 

                                 Slow /Fast time

                              ━━━━━━━━━ x Total Time 

                                Slow + Fast Time 

                       5

               =  ━━━ x 48 Hours                       [Sunday 5 PM to Tuesday 5 PM = 48 Hours]

                      12

             = 5 x 4 Hours 

             = 20 hours

           After 20 hours of Sunday 5 PM, Clock depicts Correct Time.

           Hence,   Sunday 5 PM + 20 Hours = Monday 1 PM


Example : A clock which loss uniformly is 5 minutes fast on Sunday 5 PM if it is 7 minutes slow on Monday  6 PM then when was it correct ?

Sol : On Sunday 5 PM  → 5 Minutes Fast

         On Monday 6 PM → 7 Minutes Slow

         We know that 

                                 Slow /Fast time

                              ━━━━━━━━━ x Total Time 

                                Slow + Fast Time 

                       5

               =  ━━━ x 25 Hours                       [Sunday 5 PM to Monday 6 PM = 25 Hours]

                      12

                        5

             = 10 ━━━Hours 

                        12

                           5

            = 10 + ━━━ x 60 

                          12

            = 10 Hours  25 Minutes  

           After 10 Hours  25 Minutes of Sunday 5 PM, Clock depicts Correct Time.

           Hence,   Sunday 5 PM + 10 Hours  25 Minutes = Monday 3 : 25 AM


Example : A clock which loss uniformly is 9 minutes fast on Sunday 5 PM if it is 3 minutes slow on Wednesday  5 AM then when was it correct ?

Sol : On Sunday 5 PM  → 9 Minutes Fast

         On Wednesday 5 PM → 3 Minutes Slow

         We know that 

                                 Slow /Fast time

                              ━━━━━━━━━ x Total Time 

                                Slow + Fast Time 

                       9

               =  ━━━ x 60 Hours                       [Sunday 5 PM to Wednesday 5 PM = 60 Hours]

                      12

               =  9 x 5 Hours

               = 45 Hours       

           After 45 hours of Sunday 5 PM, Clock depicts Correct Time.

           Hence,   Sunday 5 PM + 45 Hours = Tuesday 2 PM        

   

TYPE 3:

Example : A clock which gains 1 hour in every 24 hours is set right on Sunday 6 PM then what will be the actual time when the clock indicates Tuesday 8 PM ?

Sol : 

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