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).









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    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. 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. 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. 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. 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