Speed, Time and Distance


  1. A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is









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    Time taken in walking both ways = 7 hours 45 minutes   ....(i)
    Time taken in walking one way and riding back = 6 hours 15 minutes   ....(ii)
    By equation (ii) × 2 – (i), we have Time taken by the man to ride both ways
    = 12 hours 30 minutes – 7 hours 45 minutes
    = 4 hours 45 minutes

    Correct Option: C

    Time taken in walking both ways = 7 hours 45 minutes   ....(i)
    Time taken in walking one way and riding back = 6 hours 15 minutes   ....(ii)
    By equation (ii) × 2 – (i), we have Time taken by the man to ride both ways
    = 12 hours 30 minutes – 7 hours 45 minutes
    = 4 hours 45 minutes


  1. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed (in km/hr) is









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    Abhay’s speed = x kmph
    Sameer’s speed = y kmph

    ∴ 
    30
    30
    = 2   ...(i)
    xy

    and,  
    30
    30
    = 1   ...(ii)
    y2x

    On adding,
    30
    30
    = 3
    x2x

    ⇒ 
    60 − 30
    = 3
    2x

    ⇒ 
    30
    = 3 ⇒ 6x = 30
    2x

    ⇒  x = 5 kmph

    Correct Option: A

    Abhay’s speed = x kmph
    Sameer’s speed = y kmph

    ∴ 
    30
    30
    = 2   ...(i)
    xy

    and,  
    30
    30
    = 1   ...(ii)
    y2x

    On adding,
    30
    30
    = 3
    x2x

    ⇒ 
    60 − 30
    = 3
    2x

    ⇒ 
    30
    = 3 ⇒ 6x = 30
    2x

    ⇒  x = 5 kmph



  1. A and B started at the same time from the same place for a certain destination.
    B walking at
    5
    of A’s speed reached the destination
    6
    1 hour 15 minutes after A. B reached the destination in









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    1 −
    5
    of time taken by B
    6

    =1 hour 15 minutes
    ∴  Time taken by B
    = 1 hour 15 minutes × 6
    =7 hours 30 minutes

    Correct Option: C

    1 −
    5
    of time taken by B
    6

    =1 hour 15 minutes
    ∴  Time taken by B
    = 1 hour 15 minutes × 6
    =7 hours 30 minutes


  1. Ram arrives at a Bank 15 minutes earlier than scheduled time if he drives his car at 42 km/hr. If he drives car at 35 km/hr he arrives 5 minutes late. The distance of the Bank from his starting point is









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    Let the required distance be x km.
    Difference of time = 15 + 5 = 20 minutes

    =
    1
    hour
    3

    According to the question,
    x
    x
    =
    1
    6x − 5x
    =
    1
    354232103

    ⇒ 
    x
    =
    1
    2103

    ⇒   x =
    210
    = 70 km.
    3

    Correct Option: A

    Let the required distance be x km.
    Difference of time = 15 + 5 = 20 minutes

    =
    1
    hour
    3

    According to the question,
    x
    x
    =
    1
    6x − 5x
    =
    1
    354232103

    ⇒ 
    x
    =
    1
    2103

    ⇒   x =
    210
    = 70 km.
    3



  1. Two guns are fired from the same place at an interval of 6 minutes. A person approaching the place observes that 5 minutes 52 seconds have elapsed between the hearing of the sound of the two guns. If the velocity of the sound is 330 m/sec, the man was approaching that place at what speed (in km/hr) ?









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    Difference of time
    = 6 min. – 5 min. 52 sec.
    = 8 seconds
    Distance covered by man in 5 min.52 seconds
    = Distance covered by sound in 8 seconds
    = 330 × 8 = 2640 m.

    ∴ Speed of man =
    2640 m
    5 min. 52 sec.

    =
    2640
    m/sec
    352

    =
    2640
    ×
    18
    kmph
    3525

    = 27 kmph

    Correct Option: B

    Difference of time
    = 6 min. – 5 min. 52 sec.
    = 8 seconds
    Distance covered by man in 5 min.52 seconds
    = Distance covered by sound in 8 seconds
    = 330 × 8 = 2640 m.

    ∴ Speed of man =
    2640 m
    5 min. 52 sec.

    =
    2640
    m/sec
    352

    =
    2640
    ×
    18
    kmph
    3525

    = 27 kmph