Speed, Time and Distance


  1. In a race of one kilometre, A gives B a start of 100 metres and still wins by 20 seconds. But if A gives B a start of 25 seconds, B wins by 50 metres. The time taken by A to run one kilometre is
    1. 17 seconds
    2. 500
      seconds
      29
    3. 1200
      seconds
      29
    4. 700
      seconds
      29

  1. View Hint View Answer Discuss in Forum

    Let A take x seconds in covering 1000m and b takes y seconds
    According to the question,

    x + 20 =
    900
    y
    1000

    ⇒  x + 20 =
    9y
       ...(i)
    10

    and, 
    950
    x + 25 = y     ...(ii)
    1000

    From equation (i),
    10x
    +
    200
    = y
    99

    ⇒  
    10x
    +
    200
    =
    950x
    + 25
    991000

    ⇒  
    10x
    +
    200
    =
    19x
    + 25
    9920

    ⇒  
    10x
    19x
    = 25 −
    200
    9209

    =
    200x − 171x
    =
    225 − 200
    1809

    ⇒ 
    29x
    =
    25
    1809

    ⇒  x =
    25
    ×
    180
    =
    500
    seconds.
    92929

    Correct Option: B

    Let A take x seconds in covering 1000m and b takes y seconds
    According to the question,

    x + 20 =
    900
    y
    1000

    ⇒  x + 20 =
    9y
       ...(i)
    10

    and, 
    950
    x + 25 = y     ...(ii)
    1000

    From equation (i),
    10x
    +
    200
    = y
    99

    ⇒  
    10x
    +
    200
    =
    950x
    + 25
    991000

    ⇒  
    10x
    +
    200
    =
    19x
    + 25
    9920

    ⇒  
    10x
    19x
    = 25 −
    200
    9209

    =
    200x − 171x
    =
    225 − 200
    1809

    ⇒ 
    29x
    =
    25
    1809

    ⇒  x =
    25
    ×
    180
    =
    500
    seconds.
    92929


  1. A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in :
    1. 18 minutes
    2. 24 minutes
    3. 16 minutes
    4. 12 minutes

  1. View Hint View Answer Discuss in Forum

    Ratio of the speed of A, B and
    C = 6 : 3 : 1
    ⇒  Ratio of the time taken

    =
    1
    :
    1
    : 1 = 1 : 2 : 6
    63

    ∴ Time taken by A =
    72
    = 12 minutes
    6

    Correct Option: D

    Ratio of the speed of A, B and
    C = 6 : 3 : 1
    ⇒  Ratio of the time taken

    =
    1
    :
    1
    : 1 = 1 : 2 : 6
    63

    ∴ Time taken by A =
    72
    = 12 minutes
    6



  1. In a one-kilometre race A, B and C are the three participants. A can give B a start of 50 m. and C a start of 69 m. The start, which B can allow C is
    1. 17 m.
    2. 20 m.
    3. 19 m.
    4. 18 m.

  1. View Hint View Answer Discuss in Forum

    Let the time taken to complete the race by A,B, and C be x minutes.

    ∴  Speed of A =
    100
    ,
    x

    B =
    1000 − 50
    =
    950
    xx

    C =
    1000 − 69
    =
    931
    xx

    Now, time taken to complete the race by
    B =
    1000
    =
    1000 × x
    950/x950

    and distance travelled by C in
    1000x
    min
    950

    =
    1000x
    ×
    931
    = 980 km.
    950x

    ∴  B can allow C
    = 1000 – 980 = 20 m

    Correct Option: B

    Let the time taken to complete the race by A,B, and C be x minutes.

    ∴  Speed of A =
    100
    ,
    x

    B =
    1000 − 50
    =
    950
    xx

    C =
    1000 − 69
    =
    931
    xx

    Now, time taken to complete the race by
    B =
    1000
    =
    1000 × x
    950/x950

    and distance travelled by C in
    1000x
    min
    950

    =
    1000x
    ×
    931
    = 980 km.
    950x

    ∴  B can allow C
    = 1000 – 980 = 20 m


  1. A train 110 metre long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
    1. 5 seconds
    2. 6 seconds
    3. 7 seconds
    4. 10 seconds

  1. View Hint View Answer Discuss in Forum

    Relative speed of train
    = (60 + 6) kmph.

    =
    66 × 5
    m/sec.
    18

    =
    55
    m/sec.
    3

    Length of train = 110 metre
    ∴   Required time =
    110
    seconds
    55/3

    =
    110 × 3
    seconds
    55

    = 6 seconds

    Correct Option: B

    Relative speed of train
    = (60 + 6) kmph.

    =
    66 × 5
    m/sec.
    18

    =
    55
    m/sec.
    3

    Length of train = 110 metre
    ∴   Required time =
    110
    seconds
    55/3

    =
    110 × 3
    seconds
    55

    = 6 seconds



  1. The time for a train of length 110 metre running at the speed of 72 km/hr to cross a bridge of length 132 metre is
    1. 9.8 seconds
    2. 12.1 seconds
    3. 12.42 seconds
    4. 14.3 seconds

  1. View Hint View Answer Discuss in Forum

    Speed of train = 72 kmph.

    =
    72 × 5
    m./sec.
    18

    = 20 m./sec.
    Required time =
    Length of train and bridge
    Speed of train

    =
    110 + 132
    seconds
    20

    =
    242
    seconds
    20

    = 12.1 seconds

    Correct Option: B

    Speed of train = 72 kmph.

    =
    72 × 5
    m./sec.
    18

    = 20 m./sec.
    Required time =
    Length of train and bridge
    Speed of train

    =
    110 + 132
    seconds
    20

    =
    242
    seconds
    20

    = 12.1 seconds