Skip to main content

CAT Quant

CAT time, speed and distance practice questions

Time, speed and distance is one of the most reliable CAT Quant topics, and also feeds data interpretation and DILR. Everything comes from distance = speed x time, but the questions differ in what they hide: an average speed over unequal times, the relative speed of two moving objects, or the effect of a current. Practise recognising the type first and the arithmetic will follow.

Key ideas

  • Distance = speed x time. Convert km/h to m/s by multiplying by 5/18.
  • For equal distances at speeds a and b, the average speed is 2ab/(a + b), not (a + b)/2.
  • Relative speed: add speeds when objects move towards each other, subtract when they move the same way.
  • A train crossing a pole travels its own length. Crossing a platform it travels its length plus the platform.
  • Boats: downstream speed = boat + stream, upstream speed = boat - stream.

Common traps

  • Taking a simple average of two speeds when the distances are equal.
  • Forgetting to add the lengths of two trains when they cross.
  • Mixing km/h and m/s in the same equation.

Practice questions with solutions

Try each question first, then open the solution. Aim for about 90 seconds per question.

  1. A car goes uphill at 40 km/h and returns downhill over the same route at 60 km/h. What is its average speed for the round trip?

    • A 48 km/h
    • B 50 km/h
    • C 52 km/h
    • D 45 km/h
    Show answer and solution

    Answer: A. 48 km/h

    For equal distances, average speed = 2 x 40 x 60 / (40 + 60) = 48 km/h.

  2. Two trains of lengths 100 m and 150 m run in opposite directions at 54 km/h and 36 km/h. How long do they take to cross each other?

    • A 8 seconds
    • B 12 seconds
    • C 10 seconds
    • D 15 seconds
    Show answer and solution

    Answer: C. 10 seconds

    Relative speed = 90 km/h = 25 m/s. Distance = 250 m. Time = 10 s.

  3. A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. How long does it take to go 24 km upstream?

    • A 2 hours
    • B 2.4 hours
    • C 4 hours
    • D 3 hours
    Show answer and solution

    Answer: D. 3 hours

    Upstream speed = 8 km/h. Time = 24 / 8 = 3 hours.

  4. A starts a journey 2 hours before B. A travels at 40 km/h and B follows at 60 km/h. How long after B starts does B catch A?

    • A 3 hours
    • B 4 hours
    • C 5 hours
    • D 6 hours
    Show answer and solution

    Answer: B. 4 hours

    A leads by 80 km. B gains 20 km per hour, so catches up in 4 hours.

  5. A man walking at 5 km/h reaches his office 12 minutes late. Walking at 6 km/h he is 10 minutes early. How far is his office?

    • A 11 km
    • B 10 km
    • C 12 km
    • D 9 km
    Show answer and solution

    Answer: A. 11 km

    d/5 - d/6 = 22/60 hour, so d/30 = 11/30 and d = 11 km.

  6. Two people start from the same point on a circular track of length 1.2 km and run in opposite directions at 4 km/h and 6 km/h. After how many minutes do they first meet?

    • A 6 minutes
    • B 7.2 minutes
    • C 7 minutes
    • D 8 minutes
    Show answer and solution

    Answer: B. 7.2 minutes

    They close the gap at 10 km/h. Time = 1.2 / 10 hours = 0.12 hours = 7.2 minutes.

  7. A car covers a journey in 5 hours at 60 km/h. At what speed, in km/h, must it travel to cover the same journey in 4 hours?

    Type in the answer (no options).

    Show answer and solution

    Answer: 75

    Distance = 300 km. Speed = 300 / 4 = 75 km/h.

  8. A train 150 m long passes a platform 250 m long in 20 seconds. What is the speed of the train in km/h?

    Type in the answer (no options).

    Show answer and solution

    Answer: 72

    Distance = 150 + 250 = 400 m in 20 s, which is 20 m/s = 72 km/h.

Keep practising