Time, Speed & Distance Aptitude Questions with Solutions
49 Time, Speed & Distance questions with hints, worked solutions and time targets — 12 easy · 24 medium · 13 hard.
- Section: Quantitative Aptitude
- Questions: 49
- By difficulty: 12 easy · 24 medium · 13 hard
- Cost: Free, unlimited on every plan
Trains, boats and streams, relative speed, average speed.
Time, Speed & Distance: the essentials
- Distance = speed × time. From km/h to m/s, multiply by 5/18; from m/s to km/h, by 18/5.
- A train passing a pole or a person covers its own length; a platform, a bridge or another train adds that length.
- Relative speed: add for opposite directions, subtract for the same direction. Objects D apart moving towards each other meet after D/(a + b).
- Average speed: equal distances at a and b give 2ab/(a + b); three equal distances give 3/(1/a + 1/b + 1/c); equal times give (a + b)/2.
- Boats: downstream = b + s and upstream = b − s, so b = (down + up)/2 and s = (down − up)/2.
- For a fixed distance, speed and time are inversely proportional: at a/b of the usual speed, the time becomes b/a of usual.
- Late and early: at speeds s₁ < s₂ with t hours between the two arrivals, d = s₁ × s₂ × t/(s₂ − s₁). Add the minutes when one trip is late and one early; subtract when both are late.
- Stoppages: minutes stopped per hour = (speed without − speed with)/speed without × 60.
- Races: 'A beats B by x metres' means B is x metres short when A finishes.
- Circular track: first meeting after L/(a − b) in the same direction, L/(a + b) in opposite directions.
Example: a 160 m train at 90 km/h, or 25 m/s, crosses a 290 m bridge in 450/25 = 18 seconds.
Questions
- A train passes a pole Easy
A 150 m long train passes a pole in 15 seconds. What is its speed in km/h? - A train crosses a platform Easy
A 200 m train crosses a 300 m platform in 25 seconds. What is the speed of the train? - Downstream and back Medium
A boat's speed in still water is 12 km/h and the stream flows at 3 km/h. How long does the boat take to go 45 km downstream and return? - Average speed of a round trip Medium
A car travels from P to Q at 60 km/h and returns at 40 km/h. What is the average speed for the whole trip? - Two trains cross each other Medium
Two trains, 120 m and 180 m long, run towards each other at 54 km/h and 36 km/h. How long do they take to cross each other? - Ten minutes late, five minutes early Hard
Walking at 4 km/h a man reaches his office 10 minutes late; at 6 km/h he reaches 5 minutes early. How far is the office? - Converting m/s to km/h Easy
A speed of 20 m/s is equal to how many km/h? - A train crosses a pole Easy
A train 180 m long crosses a pole in 12 seconds. What is its speed? - A train crosses a bridge Medium
A train 150 m long running at 72 km/h crosses a bridge 250 m long. How long does it take? - Length of the platform Medium
A train 120 m long travelling at 54 km/h crosses a platform in 20 seconds. What is the length of the platform? - Two trains passing each other Medium
Two trains 140 m and 160 m long run towards each other at 60 km/h and 48 km/h. How long do they take to cross each other? - One train overtaking another Medium
Two trains 100 m and 150 m long run in the same direction at 72 km/h and 54 km/h. How long does the faster take to completely overtake the slower? - A train passes a running man Medium
A train 150 m long running at 68 km/h passes a man running at 8 km/h in the same direction. How long does it take? - Average speed there and back Medium
A man goes from A to B at 40 km/h and returns at 60 km/h. What is his average speed for the whole journey? - A journey in three equal parts Hard
A man covers equal distances at 10, 20 and 60 km/h. What is his average speed for the whole journey? - Late at one speed, early at another Hard
Walking at 4 km/h a man reaches his office 10 minutes late; at 6 km/h he arrives 5 minutes early. How far is the office? - Late at both speeds Hard
A boy walking at 5 km/h reaches school 6 minutes late; walking at 6 km/h he is 2 minutes late. How far is the school? - Downstream and upstream speeds Easy
A boat's speed in still water is 15 km/h and the stream flows at 3 km/h. What are its downstream and upstream speeds? - Boat and stream from two speeds Medium
A boat goes downstream at 16 km/h and upstream at 10 km/h. What is the speed of the boat in still water and of the stream? - A round trip on the river Medium
A boat whose speed in still water is 10 km/h travels 24 km downstream and back on a stream flowing at 2 km/h. How long does the whole trip take? - Still-water speed from two times Medium
A man rows 30 km downstream in 2 hours and the same distance upstream in 6 hours. What is his speed in still water? - Distance from speed and time Easy
A car travels at 60 km/h for 2 hours 30 minutes. How far does it go? - Time for a journey Easy
How long does a train take to cover 330 km at 55 km/h? - Raising the speed to save time Easy
A man covers a distance in 6 hours at 40 km/h. At what speed must he travel to cover it in 4 hours? - Two speeds on one journey Medium
A man travels the first 60 km at 30 km/h and the next 60 km at 60 km/h. What is his average speed? - Catching up Medium
A thief runs at 10 km/h and a policeman 100 metres behind chases at 12 km/h. How long does the policeman take to catch him? - Two trains meeting Easy
Two trains start at the same time from stations 330 km apart and travel towards each other at 60 km/h and 50 km/h. After how long do they meet? - Where they meet Medium
Two trains 300 km apart move towards each other at 40 km/h and 60 km/h. How far from the first station do they meet? - A race with a head start Medium
In a 100 m race A beats B by 10 metres. If A's speed is 10 m/s, what is B's speed? - Beaten by a distance and a time Hard
In a 200 m race A beats B by 20 metres or 5 seconds. What is A's time for the race? - Meeting on a circular track Medium
Two runners on a 400 m circular track run in the same direction at 5 m/s and 3 m/s. After how long do they first meet again? - Opposite directions on a track Medium
Two runners start together on a 600 m circular track in opposite directions at 4 m/s and 6 m/s. After how long do they first meet? - A slower speed costs time Hard
A train travelling at 60 km/h reaches its destination on time. If it runs at 50 km/h it arrives 20 minutes late. What is the distance? - Walking one way, riding the other Hard
A man walks to a place and rides back, taking 5 hours 45 minutes in all. He could have ridden both ways in 4 hours. How long would he take to walk both ways? - Stoppages on a bus route Medium
A bus without stoppages averages 54 km/h, and with stoppages 45 km/h. For how many minutes per hour does the bus stop? - Half the distance at each speed Hard
A man covers half a journey at 30 km/h and the other half at 20 km/h, taking 10 hours in all. What is the total distance? - Two trains, one pole Hard
A train passes a pole in 15 seconds and a platform 100 m long in 25 seconds. What is the length of the train? - Ratio of speeds to ratio of times Easy
The speeds of two cars are in the ratio 4 : 5. What is the ratio of the times they take to cover the same distance? - Two cars, same road Medium
Two cars cover the same distance, one at 45 km/h and the other at 60 km/h. The slower takes 1 hour longer. What is the distance? - A cyclist overtakes a walker Hard
A walker leaves at 6 a.m. at 5 km/h. A cyclist leaves the same point at 8 a.m. at 15 km/h along the same road. At what time does the cyclist catch up? - Upstream takes twice as long Medium
A man takes twice as long to row upstream as downstream. If the stream flows at 3 km/h, what is his speed in still water? - A train and two people Hard
A train passes two people walking in the same direction at 2 km/h and 4 km/h in 9 and 10 seconds respectively. What is the speed of the train? - Distance in minutes Easy
A cyclist rides at 18 km/h. How far does he travel in 40 minutes? - Making up lost time Medium
A man covers two-thirds of a 120 km journey at 20 km/h. At what speed must he cover the rest to complete the whole journey in 5 hours? - Walking up a moving escalator Hard
A man walking up a stationary escalator takes 90 seconds. The escalator moving with him standing still takes 60 seconds. - Two speeds, one round trip Medium
A man goes to a place at 12 km/h and returns at 8 km/h, taking 10 hours in all. What is the one-way distance? - Travelling at a fraction of the usual speed Hard
Walking at three-quarters of his usual speed, a man reaches his office 20 minutes late. What is his usual time for the journey? - Crossing a bridge on foot Easy
A man walking at 5 km/h crosses a bridge in 15 minutes. What is the length of the bridge? - Equal lengths, different speeds Medium
Two trains of equal length 120 m run on parallel tracks at 42 km/h and 30 km/h in the same direction. How long does the faster take to pass the slower?
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