Speed, Time and Distance


  1. A train starts from A at 7 a.m. towards B with speed 50 km/h. Another train starts from B at 8 a.m. with speed 60 km/h towards A. Both of them meet at 10 a.m. at C. The ratio of the distance AC to BC is
    1. 5 : 6
    2. 5 : 4
    3. 6 : 5
    4. 4 : 5

  1. View Hint View Answer Discuss in Forum


    AC = Distance covered by train starting from A in 3 hours
    = 50 × 3 = 150 km
    BC = Distance covered by train starting from B in 2 hours
    = 60 ×2 = 120 km
    ∴  AC : BC = 150 : 120 = 5 : 4

    Correct Option: B


    AC = Distance covered by train starting from A in 3 hours
    = 50 × 3 = 150 km
    BC = Distance covered by train starting from B in 2 hours
    = 60 ×2 = 120 km
    ∴  AC : BC = 150 : 120 = 5 : 4


  1. The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6 : 5. The ratio of time
    taken by them to cross a pole is
    1. 5 : 6
    2. 11 : 8
    3. 25 : 18
    4. 27 : 16

  1. View Hint View Answer Discuss in Forum

    Required ratio

    =
    5
    :
    3
    =
    30 × 5
    :
    30 × 3
    6565

    = 25 : 18

    Correct Option: C

    Required ratio

    =
    5
    :
    3
    =
    30 × 5
    :
    30 × 3
    6565

    = 25 : 18



  1. The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination ?
    1. 1
      1
      hours
      3
    2. 2 hours
    3. 2
      2
      hours
      3
    4. 1
      2
      hours
      3

  1. View Hint View Answer Discuss in Forum

    Ratio of speed = 3 : 4
    Ratio of time taken = 4 : 3
    Let the time taken by A and B be 4x hours and 3 x hours respectively.

    Then, 4x–3x =
    20
    ⇒ x =
    1
    603

    ∴  Time taken by A = 4x hours
    = 4 ×
    1
    hours
    3

    = 1
    1
    hours
    3


    Second Method :
    Here, S1 = 3x, S2 = 4x
    t2= y, t1 = y +
    20
    = y +
    1
    603

    S1t1 = S2t2
    3x y +
    1
    = 4xy
    3

    ∴  Time taken by A = 1 +
    1
    = 1
    1
    hours
    33

    Correct Option: A

    Ratio of speed = 3 : 4
    Ratio of time taken = 4 : 3
    Let the time taken by A and B be 4x hours and 3 x hours respectively.

    Then, 4x–3x =
    20
    ⇒ x =
    1
    603

    ∴  Time taken by A = 4x hours
    = 4 ×
    1
    hours
    3

    = 1
    1
    hours
    3


    Second Method :
    Here, S1 = 3x, S2 = 4x
    t2= y, t1 = y +
    20
    = y +
    1
    603

    S1t1 = S2t2
    3x y +
    1
    = 4xy
    3

    ∴  Time taken by A = 1 +
    1
    = 1
    1
    hours
    33


  1. In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :
    1. 1 hour
    2. 1
      1
      hours
      2
    3. 2 hours
    4. 2
      1
      hours
      2

  1. View Hint View Answer Discuss in Forum

    Let the distance of destination be D km
    Let the speed of A = 3x km/hr
    then speed of B = 4x km/hr
    ∴  According to question,

    D
    D
    = 30 minutes
    3x4x

    =
    1
    hr
    2

    ∴ 
    D
    =
    1
    12x2

    ⇒ 
    D
    =
    4
    = 2 hours
    3x2

    Hence, time taken by A to reach
    destination = 2hrs.

    Second Method :
    Here, S1 = 3x, S2 = 4x
    t2= y, t1 = y +
    30
    = y +
    1
    602

    S1t1 = S2t2
    3x × y +
    1
    = 4 x × y
    2

    3y +
    3
    = 4y
    2

    y =
    3
    2

    ∴  Time taken by A =
    3
    +
    1
    = 2 hrs.
    22

    Correct Option: C

    Let the distance of destination be D km
    Let the speed of A = 3x km/hr
    then speed of B = 4x km/hr
    ∴  According to question,

    D
    D
    = 30 minutes
    3x4x

    =
    1
    hr
    2

    ∴ 
    D
    =
    1
    12x2

    ⇒ 
    D
    =
    4
    = 2 hours
    3x2

    Hence, time taken by A to reach
    destination = 2hrs.

    Second Method :
    Here, S1 = 3x, S2 = 4x
    t2= y, t1 = y +
    30
    = y +
    1
    602

    S1t1 = S2t2
    3x × y +
    1
    = 4 x × y
    2

    3y +
    3
    = 4y
    2

    y =
    3
    2

    ∴  Time taken by A =
    3
    +
    1
    = 2 hrs.
    22



  1. In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :
    1. 1 hour
    2. 1
      1
      hours
      2
    3. 2 hours
    4. 2
      1
      hours
      2

  1. View Hint View Answer Discuss in Forum

    Let the distance of destination be D km
    Let the speed of A = 3x km/hr
    then speed of B = 4x km/hr
    ∴  According to question,

    D
    D
    = 30 minutes
    3x4x

    =
    1
    hr
    2

    ∴ 
    D
    =
    1
    12x2

    ⇒ 
    D
    =
    4
    = 2 hours
    3x2

    Hence, time taken by A to reach
    destination = 2hrs.

    Second Method :
    Here, S1 = 3x, S2 = 4x
    t2= y, t1 = y +
    30
    = y +
    1
    602

    S1t1 = S2t2
    3x × y +
    1
    = 4 x × y
    2

    3y +
    3
    = 4y
    2

    y =
    3
    2

    ∴  Time taken by A =
    3
    +
    1
    = 2 hrs.
    22

    Correct Option: C

    Let the distance of destination be D km
    Let the speed of A = 3x km/hr
    then speed of B = 4x km/hr
    ∴  According to question,

    D
    D
    = 30 minutes
    3x4x

    =
    1
    hr
    2

    ∴ 
    D
    =
    1
    12x2

    ⇒ 
    D
    =
    4
    = 2 hours
    3x2

    Hence, time taken by A to reach
    destination = 2hrs.

    Second Method :
    Here, S1 = 3x, S2 = 4x
    t2= y, t1 = y +
    30
    = y +
    1
    602

    S1t1 = S2t2
    3x × y +
    1
    = 4 x × y
    2

    3y +
    3
    = 4y
    2

    y =
    3
    2

    ∴  Time taken by A =
    3
    +
    1
    = 2 hrs.
    22