Speed and distance

2011 · Q41

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: 8UPSC key
3. (c)4: 5
4. (d)1: 2

2012 · Q24

Mr. Kumar drives to work at an average speed of 48 km per hour. 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 kmUPSC key
3. (c)45 km
4. (d)48 km

2013 · Q35

A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 m ahead of the policeman, then the time required for the policeman to catch the thief will be

1. (a)2 min
2. (b)3 minUPSC key
3. (c)4 min
4. (d)6 min

2013 · Q36

A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original speed of the train in km/hr?

1. (a)24
2. (b)33
3. (c)42UPSC key
4. (d)66

2013 · Q66

A person can walk a certain distance and drive back in six hours. He can also walk both ways in 10 hours. How much time will he take to drive both ways?

1. (a)Two hoursUPSC key
2. (b)Two and a half hours
3. (c)Five and a half hours
4. (d)Four hours

2014 · Q50

A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is

1. (a)3 km
2. (b)4 km
3. (c)5 kmUPSC key
4. (d)6 km

2014 · Q69

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 AMUPSC key
2. (b)10: 30 AM
3. (c)11: 10 AM
4. (d)11: 20 AM

2015 · Q34

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 speeds of A to B assuming that both start at the same time?

1. (a)25: 21UPSC key
2. (b)25: 20
3. (c)5: 3
4. (d)5: 7

2015 · Q71

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?

1. (a)45 km/hr
2. (b)48 km/hrUPSC key
3. (c)50 km/hr
4. (d)55 km/hr

2016 · Q75

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)7UPSC key
2. (b)6
3. (c)5
4. (d)8

2017 · Q39

A freight train left Delhi for Mumbai at an average speed of 40 km/hr. Two hours later, an express train left Delhi for Mumbai, following the freight train on a parallel track at an average speed of 60 km/hr. How far from Delhi would the express train meet the freight train?

1. (a)480 km
2. (b)260 km
3. (c)240 kmUPSC key
4. (d)120 km

2018 · Q5

The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where perpendicular from P meets the horizontal line CKD such that PD = ($\dfrac{1}{2}$)LD:

What is the ratio between the distances covered by vehicles A and B in the time interval OL?

1. (a)1: 2
2. (b)2: 3
3. (c)3: 4UPSC key
4. (d)1: 1

2018 · Q6

A train 200 metres long is moving at the rate of 40 kmph. In how many seconds will it cross a man standing near the railway line?

1. (a)12
2. (b)15
3. (c)16
4. (d)18UPSC key

2018 · Q40

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° 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: 5UPSC key
2. (b)4: 3
3. (c)6: 1
4. (d)4: 2

2019 · Q36

X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?

1. (a)20
2. (b)25UPSC key
3. (c)30
4. (d)35

2020 · Q72

A car travels from a place X to place Y at an average speed of v km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey

1. (a)is less than v km/hr
2. (b)lies between v and 2v km/hrUPSC key
3. (c)lies between 2v and 3v km/hr
4. (d)lies between 3v and 4v km/hr

2020 · Q74

A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?

1. (a)1: 2
2. (b)2: 1
3. (c)1: 3
4. (d)3: 1UPSC key

2021 · Q29

A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1·5 km/hr and Y walks with a uniform speed of 1 km/hr in the first hour, with a uniform speed of 1·25 km/hr in the second hour and with a uniform speed of 1·5 km/hr in the third hour and so on.

Which of the following is/are correct?

1.They take 5 hours to meet.

2.They meet midway between A and B.

Select the correct answer using the code given below:

1. (a)1 only
2. (b)2 only
3. (c)Both 1 and 2UPSC key
4. (d)Neither 1 nor 2

2022 · Q15

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)3UPSC key
3. (c)4
4. (d)5

2022 · Q46

A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1·25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is

1. (a)10 minutes slow
2. (b)5 minutes slow
3. (c)10 minutes fast
4. (d)5 minutes fastUPSC key

2025 · Q37

P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?

1. (a)12
2. (b)13UPSC key
3. (c)14
4. (d)15

2025 · Q39

A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?

1. (a)15 m
2. (b)18 m
3. (c)20 mUPSC key
4. (d)24 m

2026 · Q20

The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?

1. (a)13·51
2. (b)13·65
3. (c)13·85UPSC key
4. (d)14·05

2026 · Q37

X and Y are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When X completed 7 rounds, Y did exactly 5. After completing 5 rounds, Y changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, X continued to run with the same speed. They stopped running when X completed exactly 21 rounds. How many times did X and Y meet after they had started and before they finally stopped?

1. (a)35UPSC key
2. (b)34
3. (c)31
4. (d)29

2026 · Q41

An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30 m/s, at what time did the explosion take place? Assume that the speed of sound is 300 m/s.

1. (a)4:59:00 PM
2. (b)4:59:02 PM
3. (c)4:58:42 PMUPSC key
4. (d)4:56:32 PM

2026 · Q50

X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?

1. (a)3
2. (b)4
3. (c)5
4. (d)6UPSC key

2026 · Q69

A train has to complete a journey of 800 km. If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing speed. On its way, the train meets with a minor accident after 200 km; and 400 km thereafter, it develops a mechanical defect. Had the train developed the mechanical defect after 200 km and met the minor accident 400 km thereafter, it would have taken 4 more hours to reach its destination. What was the original speed of the train in km per hour?

1. (a)200UPSC key
2. (b)190
3. (c)150
4. (d)100