Time, Speed & Distance

Ladakh Police Sub-Inspector · Mathematics · 44 practice questions with answers and explanations: 15 Easy, 26 Medium, 3 Hard.

Sample questions

Sample Easy question 1

A cyclist travels at 15 km/h for 3 hours. Find the distance covered.

  1. 45 km
  2. 40 km
  3. 48 km
  4. 42 km
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Answer: A. Distance = speed × time = 15 × 3 = 45 km.

Sample Easy question 2

A car needs to cover 180 km at a speed of 45 km/h. Find the time taken.

  1. 4.5 hours
  2. 3.5 hours
  3. 3 hours
  4. 4 hours
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Answer: D. Time = distance/speed = 180/45 = 4 hours.

Sample Easy question 3

Convert a speed of 54 km/h into metres per second.

  1. 12 m/s
  2. 15 m/s
  3. 20 m/s
  4. 18 m/s
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Answer: B. Speed in m/s = km/h × 5/18 = 54 × 5/18 = 15 m/s.

Sample Medium question 4

Sandeep, while going to school, walks at 9/10 of his usual speed and reaches 6 minutes late. Find his usual time to reach school.

  1. 60 minutes
  2. 6 minutes
  3. 51 minutes
  4. 54 minutes
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Answer: D. Speed ratio = 10 : 9 (usual : reduced), so time ratio = 9 : 10. The 1 part of the time difference equals 6 min, so usual time (9 parts) = 54 minutes.

Sample Medium question 5

Arjun, while going to college, walks at 9/10 of his usual speed and reaches 10 minutes late. Find his usual time to reach college.

  1. 10 minutes
  2. 85 minutes
  3. 100 minutes
  4. 90 minutes
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Answer: D. Speed ratio = 10 : 9 (usual : reduced), so time ratio = 9 : 10. The 1 part of the time difference equals 10 min, so usual time (9 parts) = 90 minutes.

Sample Medium question 6

Meera, while going to school, walks at 9/10 of his usual speed and reaches 6 minutes late. Find his usual time to reach school.

  1. 51 minutes
  2. 54 minutes
  3. 6 minutes
  4. 60 minutes
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Answer: B. Speed ratio = 10 : 9 (usual : reduced), so time ratio = 9 : 10. The 1 part of the time difference equals 6 min, so usual time (9 parts) = 54 minutes.

Sample Hard question 7

A train overtakes two persons walking in the same direction at 3 km/h and 5 km/h respectively, and passes them in 10 and 11 seconds respectively. Find the speed of the train (in km/h).

  1. 27 km/h
  2. 23 km/h
  3. 25 km/h
  4. 29 km/h
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Answer: C. Since the train's length L is the same in both cases: (V-3)×10 = (V-5)×11 (using relative speed × time). This gives 10V-30 = 11V-55, so V = 25 km/h.

Sample Hard question 8

A thief is spotted by a policeman 200 m away. When the policeman starts chasing, the thief also starts running. If the thief's speed is 8 km/h and the policeman's speed is 10 km/h, find the distance the thief runs before being caught.

  1. 900 m
  2. 800 m
  3. 850 m
  4. 750 m
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Answer: B. Relative speed = 10-8 = 2 km/h. Time to close 200 m (0.2 km) gap = 0.2/2 = 0.1 hours. Distance thief runs = 8 × 0.1 = 0.8 km = 800 m.

Sample Hard question 9

Walking at 5 km/h, a man is 6 minutes late; walking at 6 km/h, he is 2 minutes early. Find the distance to his destination.

  1. 4 km
  2. 4.5 km
  3. 3 km
  4. 3.5 km
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Answer: A. The time difference is 8 minutes = 8/60 hr; solving d/5 - d/6 = 8/60 gives d = 4 km.

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