Time, Speed & Distance

Ladakh Prison Department · Mathematics · 44 practice questions with answers and explanations: 15 Easy, 26 Medium, 3 Hard.

Sample questions

Sample Easy question 1

Two cars start from the same point at the same time, traveling in the same direction at 40 km/h and 55 km/h. After how long will they be 60 km apart?

  1. 4 hrs
  2. 4.5 hrs
  3. 3 hrs
  4. 3.5 hrs
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Answer: A. Relative speed = 15 km/h; time = 60/15 = 4 hours.

Sample Easy question 2

A car covers 240 km in 4 hours. Find its speed.

  1. 58 km/h
  2. 65 km/h
  3. 55 km/h
  4. 60 km/h
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Answer: D. Speed = distance/time = 240/4 = 60 km/h.

Sample Easy question 3

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 Medium question 4

Tabassum, while going to office, walks at 5/6 of his usual speed and reaches 36 minutes late. Find his usual time to reach office.

  1. 180 minutes
  2. 162 minutes
  3. 36 minutes
  4. 216 minutes
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Answer: A. Speed ratio = 6 : 5 (usual : reduced), so time ratio = 5 : 6. The 1 part of the time difference equals 36 min, so usual time (5 parts) = 180 minutes.

Sample Medium question 5

Rohan, while going to the station, walks at 5/6 of his usual speed and reaches 20 minutes late. Find his usual time to reach the station.

  1. 100 minutes
  2. 90 minutes
  3. 120 minutes
  4. 20 minutes
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Answer: A. Speed ratio = 6 : 5 (usual : reduced), so time ratio = 5 : 6. The 1 part of the time difference equals 20 min, so usual time (5 parts) = 100 minutes.

Sample Medium question 6

Meera, while going to office, walks at 6/7 of his usual speed and reaches 20 minutes late. Find his usual time to reach office.

  1. 140 minutes
  2. 110 minutes
  3. 20 minutes
  4. 120 minutes
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Answer: D. Speed ratio = 7 : 6 (usual : reduced), so time ratio = 6 : 7. The 1 part of the time difference equals 20 min, so usual time (6 parts) = 120 minutes.

Sample Hard question 7

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 8

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.

Sample Hard question 9

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.

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