Speed, Time and Distance


  1. Points ‘A’ and ‘B’ are 70 km apart on a highway. A car starts from ‘A’ and another from ‘B’ at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each-other, they meet in one hour. Find the speed of the two cars (in km/hr).
    1. 20, 30
    2. 40, 30
    3. 30, 50
    4. 20, 40

  1. View Hint View Answer Discuss in Forum


    Let speed of car starting from A be x kmph
    and speed of car starting from B be y kmph
    Case I
    When cars meet at P,
    7x = AP = AB + BP = 70 + 7y
    ⇒  7x – 7y = 70
    ⇒  x – y = 10    ...(i)
    Case II
    When cars meet at Q,
    x + y = 70    ...(ii)
    On adding these equations,
    x = 40 kmph
    Putting the value of x in equation (i),
    y = 40 – 10 = 30 kmph

    Correct Option: B


    Let speed of car starting from A be x kmph
    and speed of car starting from B be y kmph
    Case I
    When cars meet at P,
    7x = AP = AB + BP = 70 + 7y
    ⇒  7x – 7y = 70
    ⇒  x – y = 10    ...(i)
    Case II
    When cars meet at Q,
    x + y = 70    ...(ii)
    On adding these equations,
    x = 40 kmph
    Putting the value of x in equation (i),
    y = 40 – 10 = 30 kmph


  1. A train crosses a pole in 15 seconds and a platform 100 metres long in 25 seconds. Its length (in metres) is
    1. 50
    2. 100
    3. 150
    4. 200

  1. View Hint View Answer Discuss in Forum

    Let the length of train be x metre.

    ∴ 
    x
    =
    x + 100
    1525

    ⇒ 
    x
    =
    x + 100
    35

    ⇒  5x = 3x + 300
    ⇒  2x = 300
    ⇒  x =
    300
    = 150 metres
    2

    Correct Option: C

    Let the length of train be x metre.

    ∴ 
    x
    =
    x + 100
    1525

    ⇒ 
    x
    =
    x + 100
    35

    ⇒  5x = 3x + 300
    ⇒  2x = 300
    ⇒  x =
    300
    = 150 metres
    2



  1. A train passes a platform 110 m long in 40 seconds and a boy standing on the platform in 30 seconds . The length of the train is
    1. 100 m
    2. 110 m
    3. 220 m
    4. 330 m

  1. View Hint View Answer Discuss in Forum

    Let the length of the train be x metres.

    Speed of train in crossing boy =
    x
    30

    Speed of train in crossing platform =
    x + 110
    40

    According to the question,
    x + 110
    =
    x
    4030

    ⇒ 
    x + 110
    =
    x
    43

    ⇒  4x = 3x + 330
    ⇒  x = 330 metres

    Correct Option: D

    Let the length of the train be x metres.

    Speed of train in crossing boy =
    x
    30

    Speed of train in crossing platform =
    x + 110
    40

    According to the question,
    x + 110
    =
    x
    4030

    ⇒ 
    x + 110
    =
    x
    43

    ⇒  4x = 3x + 330
    ⇒  x = 330 metres


  1. A moving train crosses a man standing on a platform and a bridge 300 metres long in 10 seconds and 25 seconds respectively. What will be the time taken by the train to cross a platform 200 metres long ?
    1. 16
      2
      seconds
      3
    2. 18 seconds
    3. 20 seconds
    4. 22 seconds

  1. View Hint View Answer Discuss in Forum

    Let the length of the train be x metre

    Speed of train when it crosses man =
    x
    10

    Speed of train when it crosses platform =
    x + 300
    25

    According to the question,
    Speed of train =
    x
    =
    x + 300
    1025

    ⇒  25x = 10x + 3000
    ⇒  15x = 3000
    ⇒  x =
    3000
    = 200 metres
    15

    ∴  Length of train = 200 metre
    Speed of train =
    x
    =
    200
    1010

    ∴ Time taken in crossing a 200 m long platform =
    200 + 200
    20

    = 20 seconds

    Correct Option: C

    Let the length of the train be x metre

    Speed of train when it crosses man =
    x
    10

    Speed of train when it crosses platform =
    x + 300
    25

    According to the question,
    Speed of train =
    x
    =
    x + 300
    1025

    ⇒  25x = 10x + 3000
    ⇒  15x = 3000
    ⇒  x =
    3000
    = 200 metres
    15

    ∴  Length of train = 200 metre
    Speed of train =
    x
    =
    200
    1010

    ∴ Time taken in crossing a 200 m long platform =
    200 + 200
    20

    = 20 seconds



  1. A train passes a platform 90 metre long in 30 seconds and a man standing on the platform in 15 seconds. The speed of the train is :
    1. 12.4 kmph
    2. 14.6 kmph
    3. 18.4 kmph
    4. 21.6 kmph

  1. View Hint View Answer Discuss in Forum

    Let the length of the train be x
    According to the question,

    Speed of the train =
    x + 90
    =
    x
    3015

    ⇒  x + 90 = 2x
    ⇒  x = 90 m
    ∴   Speed of train =
    90
    15

    = 6 m/s = 6 ×
    18
    kmph
    5

    = 21.6 kmph

    Correct Option: D

    Let the length of the train be x
    According to the question,

    Speed of the train =
    x + 90
    =
    x
    3015

    ⇒  x + 90 = 2x
    ⇒  x = 90 m
    ∴   Speed of train =
    90
    15

    = 6 m/s = 6 ×
    18
    kmph
    5

    = 21.6 kmph