Quantitative Aptitude

Time, Speed and Distance: Practice Questions with Answers

14 practice questions on Time, Speed and Distance, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Two trains, 150 m and 100 m long, run on parallel tracks in opposite directions at 45 km/hr and 36 km/hr respectively. In how much time will they completely cross each other?

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   Answer: 100/9 seconds ≈ 11.1 seconds

   Solution:

   1. Moving in opposite directions, relative speed = sum of speeds = 45 + 36 = 81 km/hr.
   2. Convert to m/s: 81 × 5/18 = 22.5 m/s.
   3. To completely cross each other, together they must cover a distance equal to the sum of both train lengths: 150 + 100 = 250 m.
   4. Time = Distance / Speed = 250 / 22.5 = 100/9 ≈ 11.1 seconds.

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2. Q.2

   Convert a speed of 72 km/hr into metres per second.

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   Answer: 20 m/s

   Solution:

   1. To convert km/hr to m/s, multiply by 5/18.
   2. 72 × 5/18 = 360/18
   3. = 20 m/s

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3. Q.3

   A man travels from town A to town B at 40 km/hr, and returns from B to A by the same road at 60 km/hr. Find his average speed for the entire journey.

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   Answer: 48 km/hr

   Solution:

   1. The distance each way is the same, so the simple average (40 + 60)/2 = 50 km/hr is WRONG here — that shortcut only works when the TIME spent at each speed is equal, not the distance.
   2. For two equal distances covered at speeds a and b, average speed = 2ab / (a + b).
   3. = (2 × 40 × 60) / (40 + 60)
   4. = 4,800 / 100 = 48 km/hr

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4. Q.4

   Towns A and B are 300 km apart. A car starts from A towards B at 50 km/hr at the same time as another car starts from B towards A at 70 km/hr. After how long do they meet, and how far from A?

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   Answer: They meet after 2.5 hours, 125 km from A

   Solution:

   1. Moving toward each other, combined speed = 50 + 70 = 120 km/hr.
   2. Time to meet = Distance / combined speed = 300 / 120 = 2.5 hours.
   3. Distance from A = speed from A × time = 50 × 2.5 = 125 km.

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5. Q.5

   A train's speed excluding stoppages is 60 km/hr, and its average speed including stoppages is 45 km/hr. Find the number of minutes per hour the train is stopped.

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   Answer: 15 minutes per hour

   Solution:

   1. Fraction of each hour "lost" to stoppages = 1 − (effective speed / running speed) = 1 − 45/60 = 1 − 0.75 = 0.25.
   2. Stoppage time per hour = 0.25 × 60 minutes
   3. = 15 minutes

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6. Q.6

   A man travels 60 km at 30 km/hr, and then a further 90 km at 45 km/hr. Find his average speed for the whole journey.

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   Answer: 37.5 km/hr

   Solution:

   1. The two distances (60 km and 90 km) are not equal, so the 2ab/(a + b) shortcut does not apply here — use total distance / total time instead.
   2. Time for the first part = 60/30 = 2 hours. Time for the second part = 90/45 = 2 hours.
   3. Total distance = 60 + 90 = 150 km. Total time = 2 + 2 = 4 hours.
   4. Average speed = 150 / 4 = 37.5 km/hr.

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7. Q.7

   A car travels at a constant speed of 60 km/hr. How long will it take to cover 180 km?

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   Answer: 3 hours

   Solution:

   1. Time = Distance / Speed
   2. = 180 / 60
   3. = 3 hours

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8. Q.8

   Two trains 120 m and 180 m long move in the same direction at 72 km/hr and 54 km/hr. Find the time the faster train takes to completely pass the slower one.

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   Answer: 60 seconds. Relative speed = 72−54 = 18 km/hr = 5 m/s; distance = 120+180 = 300 m; time = 300/5.

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9. Q.9

   A train covers a certain distance at 50 km/hr and returns over the same route at 75 km/hr. Find its average speed for the whole trip.

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   Answer: 60 km/hr. 2ab/(a+b) = (2×50×75)/125 = 7,500/125.

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10. Q.10

    A bus's speed excluding stoppages is 50 km/hr, and including stoppages it is 40 km/hr. Find the stoppage time per hour.

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    Answer: 12 minutes. (1 − 40/50) × 60 = 0.2 × 60.

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11. Q.11

    Two cyclists start at the same time from points 72 km apart and ride towards each other at 15 km/hr and 21 km/hr. After how long do they meet?

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    Answer: 2 hours. 72/(15+21) = 72/36.

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12. Q.12

    Convert a speed of 90 km/hr into metres per second.

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    Answer: 25 m/s. 90 × 5/18 = 25.

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13. Q.13

    A cyclist covers 150 km in 6 hours. Find his speed in km/hr.

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    Answer: 25 km/hr. Speed = 150/6.

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14. Q.14

    A man walks 20 km at 4 km/hr and then cycles 60 km at 20 km/hr. Find his average speed for the whole journey.

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    Answer: 10 km/hr. Time = 20/4 + 60/20 = 5 + 3 = 8 hours; total distance = 80 km; average = 80/8.

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