Speed, Time and Distance


  1. If a man reduces his speed to 2/3, he takes 1 hour more in walking a certain distance. The time (in hours) to cover the distance with his normal speed is :
    1. 2
    2. 1
    3. 3
    4. 1.5

  1. View Hint View Answer Discuss in Forum

    Since man walks at 2/3 of usual speed, time taken will be 3/2 of usual time.

    ∴  
    3
    of usual time = usual time + 1 hour.
    2

    ⇒  
    3
    − 1of usual time = 1
    2

    ⇒   usual time = 2 hours.

    Correct Option: A

    Since man walks at 2/3 of usual speed, time taken will be 3/2 of usual time.

    ∴  
    3
    of usual time = usual time + 1 hour.
    2

    ⇒  
    3
    − 1of usual time = 1
    2

    ⇒   usual time = 2 hours.


  1. Two trains of equal length are running on parallel lines in the same direction at 46 km/hour and 36 km/hour. The faster train passes the slower train in 36 seconds. The length of each train is
    1. 72 m
    2. 80 m
    3. 82 m
    4. 50 m

  1. View Hint View Answer Discuss in Forum

    Let the length of each train be x metre.
    Relative speed = (46 – 36) kmph = 10 kmph

    =
    10 × 5
    m./sec.
    18

    =
    25
    m./sec.
    9

    ∴ 
    2x
    = 36
    25
    9

    ∴  2x = 36 ×
    25
    = 100
    9

    ⇒  x =
    100
    = 50 metre
    2

    Correct Option: D

    Let the length of each train be x metre.
    Relative speed = (46 – 36) kmph = 10 kmph

    =
    10 × 5
    m./sec.
    18

    =
    25
    m./sec.
    9

    ∴ 
    2x
    = 36
    25
    9

    ∴  2x = 36 ×
    25
    = 100
    9

    ⇒  x =
    100
    = 50 metre
    2



  1. A thief is stopped by a policeman from a distance of 400 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 5 km/h and that of policeman as 9 km/h, how far the thief would have run, before he is over taken by the policeman ?
    1. 400 metre
    2. 600 metre
    3. 500 metre
    4. 300 metre

  1. View Hint View Answer Discuss in Forum

    Distance between thief and policeman = 400 metre
    Relative speed of policeman with respect to thief
    = (9 – 5) kmph
    = 4 kmph

    =
    4 × 5
    m./sec.
    18

    =
    10
    m./sec.
    9

    Time taken in overtaking the thief
    =
    400
    second
    10/9

    =
    400 × 9
    second
    10

    = 360 second
    ∴  Distance covered by thief
    = Speed × Time
    = 5 ×
    5
    × 360metre
    18

    = 500 metre

    Correct Option: C

    Distance between thief and policeman = 400 metre
    Relative speed of policeman with respect to thief
    = (9 – 5) kmph
    = 4 kmph

    =
    4 × 5
    m./sec.
    18

    =
    10
    m./sec.
    9

    Time taken in overtaking the thief
    =
    400
    second
    10/9

    =
    400 × 9
    second
    10

    = 360 second
    ∴  Distance covered by thief
    = Speed × Time
    = 5 ×
    5
    × 360metre
    18

    = 500 metre


  1. Two trains start from a certain place on two parallel tracks in the same direction. The speed of the trains are 45 km/hr. and 40 km/hr respectively. The distance between the two trains after 45 minutes will be
    1. 2.5 km.
    2. 2.75 km.
    3. 3.7 km.
    4. 3.75 km.

  1. View Hint View Answer Discuss in Forum

    Relative speed = 45 – 40 = 5 kmph.

    ∴  Gap between trains after 45 minutes =5 ×
    45
    km
    60

    = 3.75 km.

    Correct Option: D

    Relative speed = 45 – 40 = 5 kmph.

    ∴  Gap between trains after 45 minutes =5 ×
    45
    km
    60

    = 3.75 km.



  1. A passenger train running at the speed of 80 kms./hr leaves the railway station 6 hours after a goods train leaves and overtakes it in 4 hours. What is the speed of the goods train?
    1. 32 kmph
    2. 50 kmph
    3. 45 kmph
    4. 64 kmph

  1. View Hint View Answer Discuss in Forum

    Let the speed of goods train be x kmph.
    ∴  Distance covered by goods train in 10 hour = distance covered by passenger train in 4 hours
    ⇒  10x = 80 × 4

    ⇒  x =
    80 × 4
    = 32 kmph.
    10

    Correct Option: A

    Let the speed of goods train be x kmph.
    ∴  Distance covered by goods train in 10 hour = distance covered by passenger train in 4 hours
    ⇒  10x = 80 × 4

    ⇒  x =
    80 × 4
    = 32 kmph.
    10