Time, Speed & Distance MCQs for UPSC Prelims

66 practice questions on Time, Speed & Distance from the Quantitative Aptitude section of the UPSC Prelims syllabus. 66 come with a written explanation and 23 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

17 Easy 37 Medium 12 Hard 23 from past papers

Sample questions

Q1
Previous year question easy

Two cities A and B are 360 km apart. A car goes from A to B with a speed of 40 km/hr and returns to A with a speed of 60 km/hr. What is the average speed of the car? (a) 45 km/hr (b) 48 km/hr (c) 50 km/hr (d) 55 km/hr

  1. A 45 km/hr
  2. B 48 km/hr
  3. C 50 km/hr
  4. D 55 km/hr
Show answer and explanation

Correct answer: B - 48 km/hr

For equal distances at two speeds, the average speed is the harmonic mean: 2 x s1 x s2 / (s1 + s2) = 2 x 40 x 60 / (40 + 60) = 4800 / 100 = 48 km/hr. (Check: time A to B = 360/40 = 9 hr, time B to A = 360/60 = 6 hr; total distance 720 km in 15 hr = 48 km/hr.)

Q2
Previous year question easy

If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then what is the ratio of the distances travelled by them in one hour?

  1. A 8 : 5
  2. B 5 : 8
  3. C 4 : 5
  4. D 1 : 2
Show answer and explanation

Correct answer: B - 5 : 8

Distance per hour equals speed. Bus speed = 160 / 4 = 40 km/h. Train speed = 320 / 5 = 64 km/h. In one hour the bus covers 40 km and the train covers 64 km, so the ratio is 40 : 64. Dividing both by 8 gives 5 : 8.

Q3
Previous year question medium

Mr. Kumar drives to work at an average speed of 48 km/h. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?

  1. A 30 km
  2. B 40 km
  3. C 45 km
  4. D 48 km
Show answer and explanation

Correct answer: B - 40 km

Let the total distance be D km, covered at a constant 48 km/h. First part = 0.6D, remaining = 0.4D. Time difference = 10 minutes = 1/6 hour. So (0.6D/48) - (0.4D/48) = 1/6, i.e. (0.2D)/48 = 1/6. Then 0.2D = 48/6 = 8, giving D = 8/0.2 = 40 km. The office is 40 km away, so (b). Other options do not satisfy the 10-minute difference.

Q4
Previous year question medium

In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speed of A to B assuming that both start at the same time?

  1. A 25 : 21
  2. B 25 : 20
  3. C 5 : 3
  4. D 5 : 7
Show answer and explanation

Correct answer: A - 25 : 21

A runs the full 500 metres to win. B started 45 m ahead, so B needed only 500 - 45 = 455 m to reach the finish line, but B is still 35 m behind the finish when A wins, meaning B has covered 455 - 35 = 420 m in the same time. Since time is equal, the speed ratio equals the distance ratio: A : B = 500 : 420 = 25 : 21. Hence option (a).

Q5
Previous year question medium

A and B walk around a circular park. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 8.00 a.m. and before 9.30 a.m.?

  1. A 7
  2. B 6
  3. C 5
  4. D 8
Show answer and explanation

Correct answer: A - 7

Walking in opposite directions, their relative speed is 2 + 3 = 5 rounds per hour, so together they close one full lap (one meeting) every 1/5 hour. The duration from 8:00 a.m. to 9:30 a.m. is 1.5 hours. Number of meetings = relative rounds in that time = 5 x 1.5 = 7.5. Since meetings happen at each completed relative lap, they cross each other 7 times within the interval (the 8th crossing would occur after 9:30). Hence 7.

Q6
Previous year question hard

Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30 degrees at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?

  1. A 6 : 5
  2. B 4 : 3
  3. C 6 : 1
  4. D 4 : 2
Show answer and explanation

Correct answer: A - 6 : 5

Take A's starting point as 0 degrees. B starts 30 degrees ahead of A in the running direction. A runs to the point diametrically opposite his start, which is 180 degrees of arc, and at that instant he meets B (they are at the same point). Since B started at the 30 degrees mark and ends at the same 180 degrees meeting point, B has covered 180 - 30 = 150 degrees of arc in the same time. Equal time means the ratio of distances equals the ratio of speeds: A : B = 180 : 150 = 6 : 5. Hence (a) 6 : 5.

Q7
Previous year question easy

Two cars start towards each other, from two places A and B which are at a distance of 160 km. They start at the same time 08:10 AM. If the speeds of the cars are 50 km and 30 km per hour respectively, they will meet each other at

  1. A 10:10 AM
  2. B 10:30 AM
  3. C 11:10 AM
  4. D 11:20 AM
Show answer and explanation

Correct answer: A - 10:10 AM

Moving towards each other, the cars close the gap at their combined speed of 50 + 30 = 80 km per hour. Time to cover 160 km = 160 / 80 = 2 hours. Adding 2 hours to the 08:10 AM start gives a meeting time of 10:10 AM.

Q8
Previous year question medium

X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?

  1. A 2
  2. B 3
  3. C 4
  4. D 5
Show answer and explanation

Correct answer: B - 3

Speeds are in the ratio 3 : 2 on a 300 m loop and the race is 3 km. The faster runner X finishes 3000 m (10 laps); in that time Y covers 3000 x 2/3 = 2000 m. X gains on Y at rate k, and a pass (lapping) occurs every time the lead grows by a full lap of 300 m. The final lead when X finishes is 3000 - 2000 = 1000 m, so passes happen at leads of 300, 600 and 900 m, i.e. 3 times; the fourth pass would need a 1200 m lead which is never reached. Option (b) 3 is correct: 2 undercounts (the 900 m lead is reached at X's 2700 m mark, before the finish), while 4 and 5 require leads beyond 1000 m.

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