Speed, Time and Distance


  1. By walking
    5
    of usual speed a student
    3
    reaches school 20 minutes earlier. Find his usual time.
    1. 45 minutes
    2. 50 minutes
    3. 60 minutes
    4. None of these

  1. View Hint View Answer Discuss in Forum

    5/3 of usual speed means 3/5 of usual time as he reaches earlier.

    ∴ 
    3
    usual time + 20 minutes = Usual time
    5

    20 minutes =1 −
    3
    usual time
    5

    =
    2
    usual time
    5

    ∴   Usual time =
    20 × 5
    = 50 minutes.
    2

    Correct Option: B

    5/3 of usual speed means 3/5 of usual time as he reaches earlier.

    ∴ 
    3
    usual time + 20 minutes = Usual time
    5

    20 minutes =1 −
    3
    usual time
    5

    =
    2
    usual time
    5

    ∴   Usual time =
    20 × 5
    = 50 minutes.
    2


  1. Walking
    3
    of my usual speed, a late
    4
    is marked on my cards by 10 minutes. Find my usual time.
    1. 30 minutes
    2. 35 minutes
    3. 32 minutes
    4. 36 minutes

  1. View Hint View Answer Discuss in Forum

    Since I walk at 3/4 of my usual speed the time taken is 4/3 of my usual time.
    [∵  the speed and time are in the inverse ratio]

    ∴ 
    4
    of usual time
    3

    = Usual time + Time I reach late
    ∴ 
    1
    of usual time
    3

    = 10 minutes
    ∴  Usual time
    = 10 × 3 = 30 minutes.

    Correct Option: A

    Since I walk at 3/4 of my usual speed the time taken is 4/3 of my usual time.
    [∵  the speed and time are in the inverse ratio]

    ∴ 
    4
    of usual time
    3

    = Usual time + Time I reach late
    ∴ 
    1
    of usual time
    3

    = 10 minutes
    ∴  Usual time
    = 10 × 3 = 30 minutes.



  1. A man has to reach a place 40 kms away. He walks at the rate of 4 km per hr. for the first 16 kms and then he hires a rickshaw for the rest of the journey. However if he had travelled by the rickshaw for the first 16 kms and the remaining distance on foot at 4 km per hr, he would have taken an hour longer to complete the journey. Find the speed of rickshaw.
    1. 6.5 kmph
    2. 7.5 kmph
    3. 6 kmph
    4. 8 kmph

  1. View Hint View Answer Discuss in Forum

    Let the speed of Rickshaw be 'x ' .
    Then, time taken to cover 16 km on foot and 24 km on Rikshaw

    =
    16
    +
    24
    hrs
    4x

    and time taken to travel 24 km on foot & 16 km on Rikshaw
    =
    16
    +
    24
    hrs
    x4

    According to question,
    =
    16
    +
    24
    + 1 =
    16
    +
    24
    4xx4

    ⇒ 
    5 + 24
    =
    16
    + 6
    xx

    ⇒ 
    24 − 16
    = 1
    x

    ⇒  x = 8 km/hr

    Correct Option: D

    Let the speed of Rickshaw be 'x ' .
    Then, time taken to cover 16 km on foot and 24 km on Rikshaw

    =
    16
    +
    24
    hrs
    4x

    and time taken to travel 24 km on foot & 16 km on Rikshaw
    =
    16
    +
    24
    hrs
    x4

    According to question,
    =
    16
    +
    24
    + 1 =
    16
    +
    24
    4xx4

    ⇒ 
    5 + 24
    =
    16
    + 6
    xx

    ⇒ 
    24 − 16
    = 1
    x

    ⇒  x = 8 km/hr


  1. If a boy walks from his house to school at the rate of 4 km per hr, he reaches the school 10 minutes earlier than the scheduled time. However if he walks at the rate of 3 km per hr, he reaches 10 minutes late. Find the distance of his school from his house.
    1. 3.5 km
    2. 3 km
    3. 4 km
    4. 4.5 km

  1. View Hint View Answer Discuss in Forum

    Let the distance be x kms.
    ∴  Time taken at 4 km per hr. t1

    =
    x
    hrs.
    4

    Time taken at 3 km per hr.t2
    =
    x
    hrs.
    3

    Difference in timings
    = 10 + 10 = 20 minutes
    or  
    20
    =
    1
    hour
    60 3

    ∴ 
    x
    x
    =
    1
    343

    ⇒ 
    4x − 3x
    =
    1
    123

    ⇒ 
    x
    =
    1
    123

    ∴  x = 4 km.
    Hence the required distance
    = 4 kms.

    Correct Option: C

    Let the distance be x kms.
    ∴  Time taken at 4 km per hr. t1

    =
    x
    hrs.
    4

    Time taken at 3 km per hr.t2
    =
    x
    hrs.
    3

    Difference in timings
    = 10 + 10 = 20 minutes
    or  
    20
    =
    1
    hour
    60 3

    ∴ 
    x
    x
    =
    1
    343

    ⇒ 
    4x − 3x
    =
    1
    123

    ⇒ 
    x
    =
    1
    123

    ∴  x = 4 km.
    Hence the required distance
    = 4 kms.



  1. A car can finish a certain journey in 10 hours at a speed of 48 km per hr. In order to cover the same distance in 8 hours, how much the speed be increased by ?
    1. 10 kmph
    2. 12 kmph
    3. 14 kmph
    4. 15 kmph

  1. View Hint View Answer Discuss in Forum

    Time = 10 hours,
    Speed = 48 km per hr.
    ∴  Distance = Speed × Time
    = 48 × 10 = 480 km
    Now, this distance of 480 kms is to be covered in 8 hours.
    Hence, the required Speed

    =
    Distance
    =
    480
    New time 8

    = 60 km per hr.
    ∴  Increase in speed
    = 60 – 48 = 12 km per hr.

    Correct Option: B

    Time = 10 hours,
    Speed = 48 km per hr.
    ∴  Distance = Speed × Time
    = 48 × 10 = 480 km
    Now, this distance of 480 kms is to be covered in 8 hours.
    Hence, the required Speed

    =
    Distance
    =
    480
    New time 8

    = 60 km per hr.
    ∴  Increase in speed
    = 60 – 48 = 12 km per hr.