Speed, Time and Distance


  1. A man travelled a distance of 61 km in 9 hours, partly on foot at the rate of 4 km/hr and partly on bicycle at the rate of 9 km/hr. The distance travelled on foot was
    1. 12 km
    2. 16 km
    3. 20 km
    4. 24 km

  1. View Hint View Answer Discuss in Forum

    Let man walked for t hours.
    then, t × 4 + (9 – t) × 9 = 61
    ⇒  4t + 81 – 9t = 61
    ⇒  81 – 5t = 61
    ⇒  5t = 20
    ⇒  t = 4
    ∴  Distance travelled on foot
    = 4 × 4 = 16 km.

    Correct Option: B

    Let man walked for t hours.
    then, t × 4 + (9 – t) × 9 = 61
    ⇒  4t + 81 – 9t = 61
    ⇒  81 – 5t = 61
    ⇒  5t = 20
    ⇒  t = 4
    ∴  Distance travelled on foot
    = 4 × 4 = 16 km.


  1. Ravi and Ajay start simultaneously from a place A towards B, 60 km apart. Ravi’s speed is 4 km/hr less than that of Ajay. Ajay, after reaching B, turns back and meets Ravi at a place 12 km away from B. Ravi’s speed is
    1. 12 km/hr
    2. 10 km/hr
    3. 8 km/hr
    4. 6 km/hr

  1. View Hint View Answer Discuss in Forum

    Let the speed of Ravi be x kmph
    then, Ajay’s speed = (x + 4) kmph
    Distance covered by Ajay
    = 60 + 12 = 72 km
    Distance covered by Ravi
    = 60 – 12 = 48 km.
    According to the question,

    72
    =
    48
    x + 4x

    ⇒ 
    3
    =
    2
    x + 4x

    ⇒  3x = 2x + 8
    ⇒  x = 8 kmph

    Correct Option: C

    Let the speed of Ravi be x kmph
    then, Ajay’s speed = (x + 4) kmph
    Distance covered by Ajay
    = 60 + 12 = 72 km
    Distance covered by Ravi
    = 60 – 12 = 48 km.
    According to the question,

    72
    =
    48
    x + 4x

    ⇒ 
    3
    =
    2
    x + 4x

    ⇒  3x = 2x + 8
    ⇒  x = 8 kmph



  1. P and Q are 27 km away. Two trains with speed of 24 km/hr and 18 km/hr respectively start simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is
    1. 126 km
    2. 81 km
    3. 48 km
    4. 36 km

  1. View Hint View Answer Discuss in Forum


    Let the trains meet after t hours, then
    24t – 18t = 27
    ⇒  6t = 27

    ⇒  t =
    27
    6

    =
    9
    hours
    2

    ∴ QR = 18t = 18 ×
    9
    = 81 km
    2

    Correct Option: B


    Let the trains meet after t hours, then
    24t – 18t = 27
    ⇒  6t = 27

    ⇒  t =
    27
    6

    =
    9
    hours
    2

    ∴ QR = 18t = 18 ×
    9
    = 81 km
    2


  1. From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours.
    Had A travelled with
    2
    of his speed
    3
    and B travelled with double of his speed, they would have met after 5 hours. The speed of A is
    1. 4 km/hr.
    2. 6 km/hr.
    3. 10 km/hr.
    4. 12 km/hr.

  1. View Hint View Answer Discuss in Forum


    Let the speed of A = x kmph and that of B = y kmph
    According to the question,
    x × 6 + y × 6 = 60
    ⇒  x + y = 10    ....(i)

    and,  
    2
    x × 5 + 2y × 5 = 60
    3

    ⇒  10x + 30y = 180
    ⇒  x + 3y = 18    ...(ii)
    From equations (i) × (3) – (ii)
    3x + 3y – x – 3y = 30 – 18
    ⇒  12x = 12
    ⇒  x = 6 kmph.

    Correct Option: B


    Let the speed of A = x kmph and that of B = y kmph
    According to the question,
    x × 6 + y × 6 = 60
    ⇒  x + y = 10    ....(i)

    and,  
    2
    x × 5 + 2y × 5 = 60
    3

    ⇒  10x + 30y = 180
    ⇒  x + 3y = 18    ...(ii)
    From equations (i) × (3) – (ii)
    3x + 3y – x – 3y = 30 – 18
    ⇒  12x = 12
    ⇒  x = 6 kmph.



  1. A man completed a certain journey by a car. If he covered 30% of the distance at the speed of 20km/hr, 60% of the distance at 40km/hr and the remaining distance at 10km/hr; his average speed for the whole journey was
    1. 25 km/hr
    2. 28 km/hr
    3. 30 km/hr
    4. 33 km/hr

  1. View Hint View Answer Discuss in Forum

    Let the total distance be 100 km.

    Average speed =
    Total distance covered
    Time taken

    =
    100
    3
    +
    3
    + 1
    22

    =
    100
    3 + 3 + 2
    2

    =
    100 × 2
    = 25 kmph
    8

    Correct Option: A

    Let the total distance be 100 km.

    Average speed =
    Total distance covered
    Time taken

    =
    100
    3
    +
    3
    + 1
    22

    =
    100
    3 + 3 + 2
    2

    =
    100 × 2
    = 25 kmph
    8