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# TRAINS DISTANCE SPEED TIME PROBLEMS WITH SOLUTIONS # APTITUDE TRAIN DISTANCE SPEED PROBLEMS WITH SOLUTIONS

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TRAINS DISTANCE SPEED TIME PROBLEMS

Distance (D) = Speed (S) × Time (T)

X kmph = X × 5/18 m/s
X m/s = X × 18/5 kmph

If the ratio of the speeds A & B is a : b, then the ratio of the times taken by them to cover the same distance is
= 1/a ∶ 1/b
= b : a

Suppose two trains are moving in the same directions at X m/s and Y m/s then their relative speed
= (X – Y) m/s
Suppose two trains are moving in the opposite directions at X m/s and Y m/s then their relative speed
= (X + Y) m/s
If two trains of length ‘A’ meters and ‘B’ meters are moving in the same directions at X m/s and Y m/s then the time taken by the trains to cross each other
= A+B / X− Y

If trains move in opposite direction s
= A+B / X+ Y

Distance (D) = Speed (S) Î Time (T)
X kmph = X Îá 5/18 m/s
X m/s = X Î 18/5 kmph
If the ratio of the speeds A & B is a : b, then the ratio of the times taken by them to cover the same distance is
=1/a : 1/b
= b : a
Suppose two trains are moving in the same directions at X m/s and Y m/s then their relative speed
= (X ľ Y) m/s
Suppose two trains are moving in the opposite directions at X m/s and Y m/s then their relative speed
= (X + Y) m/s
If two trains of length ĹAĺ meters and ĹBĺ meters are moving in same directions at X m/s and Y m/s then the time taken by the trains to cross each other
= A + B / X – Y seconds
If trains move in opposite direction
= A + B / X + Y seconds

Practice Problems

1) Samir drove at the speed of 45kmph from home to resort. Returning over the same route he got stuck in traffic and took an hour longer. Also, he could drive only at the speed of 40 kmph. How many kilometers did he drive each way?

2) A 320-meter long train moving an average speed of 120 kmph crosses a platform in 24 seconds. A man crosses the platform in 4 minutes. What is the speed of the man in m/s

3) A driver was supposed to drive at a uniform speed to cover a distance of 180 km, he was 54 minutes late. To cover this lost time he had to increase the speed by 10 kmph, what is the original speed

4) A car covers a certain distance taking 7 hours in a forward journey. During the return, journey speed was increased by 12 kmph and it takes 5 hours. What is the total distance ?

5) Two trains of equal length running in opposite directions, pass a pole in 18 & 12 seconds. The train will cross each other in

6) A thief seeing a policeman from a distance of 200 meters starts running with a speed of 8 kmph. The policeman gives chase immediately with a speed of 9 kmph and the thief is caught. The distance run by the thief is

7) A train moving at a rate of 36 kmph crosses a standing man in 10 seconds. It will cross a platform 55 meters long in?

8) A person travels 285 km in 6 hours. In the first part of the journey he travels at 40 kmph by bus. In the second part, he travels at 55 kmph by train. The distance travelled by train is..

9) A train overtakes two persons who are walking in the same directions in which the train is running at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train is?

10) Ramana started a journey at 1 pm at 30 kmph. Karthik started from the same spot and in the same direction at 1.40 pm at 40 kmph. Kartikovertook Ramana in?

11) A train crosses a man on the platform in 8.5 seconds and crosses the platform of 240 meters in length in 20.5 seconds. What is the length of the train?

12) A motor car does a journey in 17.5 hours covering the first half at 30 kmph and the second half at 40 kmph. Find the distance of the journey

13) A car starts from A for B travelling 20 kmph. 1 Ż hours later another car starts from A & travelling at the rate of 30 kmph reaches B, 2 Ż hours before the first car. Find the distance from A to B

14) If a man walks 20 km at 5 kmph, he will be late by 40 minutes. If he walks at 8 kmph, how early from the fixed time will he reach

15) In covering a certain distance, the speed of A & B in the ratio of 3: 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destinationůůů

16) A train covers certain distance between two places at a uniform speed. If the train moved 10 kmph faster, it would take 2 hours less. And, if the train was slower by 10 kmph, it would take 3 hours more than the scheduled time. Find the distance covered by the train

17) A train passes two bridges of lengths 800 m & 400 m in 100 seconds & 60 seconds respectively. The length of the train is

18) Two cars start at the same time from one point and move along two roads at right angle to each other. Their speeds are 36 kmph& 48 kmph respectively. After 15 seconds the distance between them will beůůů

19) Two trains start from stations A & B and travel towards each other at speeds of 50 kmph and 60 kmph respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A & B is

20) A train running at 7/11th of its own speed reached a place in 22 hours. How much time could be saved if the train would run at its own speed

21) A man can reach a certain place in 30 hours. If he reduces his speed by 1/15thá he goes 10 km less in that time. Find his speed in kmph

22) Two trains, Kolkata & Mumbai starts at the same time from stations Kolkata & Mumbai respectively towards each other. After passing each other they take 12 hours & 3 hours to reach Mumbai & Kolkata respectively. If the Kolkata train is moving at the speed of the 48 kmph, the speed of the Mumbai train is.

23) Two trains starts at the same time from Mumbai & Pune and proceed towards each other at the rate of 60 kmph& 40 kmph respectively. When they meet it is found that one train has travelled 20 km more than the other. Find the distance between Mumbai & Pune

24) A boy takes as much time in running 12 meters as a car takes in covering 36 meters. The ratio of the speeds of the boy & the car is

25) A & B are two stations. A train goes from A to B at 64 kmph and returns to A at a slower speed. If its average speed for the whole journey is 56 kmph, at what speed did it return ?

26) Amit started cycling along the boundaries of a square field from cover point A. After half an hour, he reached the corner point C, diagonally opposite to A. If his speed was 8 kmph, what is the area of the field in square

27) A train travelling at 48 kmph completely crosses another train having half it length and travelling in opposite directions at 42 kmph in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

28) A man is walking at a speed of 10 kmph. After every km, he takes a rest for 5 minutes. How much time will he take to cover a distance of 5 kmůůůů

29) In a one kilometer race, A can beat B by 30 meters while in a 500 meter race B can beat C by 25 meters. By how many meters will A beat C in a 100 meter raceůů..

30) A car covers 1/5 of the distance from A to B at the speed of 8 kmph, 1/10 of the distance at 25 kmph and remaining at the speed of 20 kmph. Find the average speed of the whole journeyůů

31) A boy started from his house by bicycle at 10 am at a speed of 12 kmph. His elder brother started after 1 hour 15 minutes by scooter along the same path and caught him at 1.30á pm. The speed of the scooter will be (kmph).

32) Buses start from a bus terminal with a speed of 20 kmph at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes

33) A railway half- ticket costs half the full rate. But the reservation charge on the half- ticket is the same as that on full ticket. One reserved full ticket for a journey between two stations is 525/- and the cost of one full and one half reserved tickets is 850/-. What is the reservation chargeůůů

34) A man travels 35 km partly at 4 kmph and at 5 kmph. If he covers former distance at 5 kmph and later distance at 4 kmph, he could cover 2 km more in the same time. The time taken to cover the whole distance at the original rate is?

35) Two persons, Ajith&Lalitha start at the same time from Secunderabad& Vijayawada and proceed towards each other at 45 kmph and 54 kmph respectively. When they meet, it is found that one of them has travelled 72 km more than the other. The distance between the placesůů..

36) The distance between two cities is 800 km. A motor car starts from the first city at the speed of 30 kmph. At the same time, another car starts from the second city towards the first city at the speed of 50 kmph. The distance of the point from the first city where both the cars meet isůůů

37) A train can travel 50% faster than a car. Both starts from point A at the same time and reach point B 75 km away from A at the same time. On the way, however the train lost about 12.5 minutes while stopping at the stations. The speed of the car isůůů..

38) In a KM race A can beat B by 80 meters and B can beat C by 60 meters. In the same race, A can beat C by

39) In a 100 meter race, A runs at 5 kmph. A gives B a start of 8 meter and still beats him by 8 seconds. Find out the speed of B

40) A can run 224 meters in 28 seconds and B in 32 seconds. By what distance A beat Bůůů..

41) The speed of a car is increased by 2 km after every hour. If the distance travelled in the first hour was 35 km, then what was the total distance travelled in 12 hoursůůů

42) A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th,á he goes 10 km less in that time. Find his speed per hourůů.

43) When a person reduces his speed from 42 kmph to 36 kmph he takes 20 minutes more than his usual time taken. Find the usual time taken by himůůůůů

44) A cyclist covers a distance of 24 km in a certain time with a certain fixed uniform speed. If he increases his speed by 2 kmph, he takes 2 hours less to cover the same distance. Find his original speed.

45) Two gunshots were fired at the interval of 12 minutes. One person moving towards the place from where gunshots were fired, listens the two sounds at the interval of 11 minutes. If the speed of sound is 330 m/s, find the speed of the person ů

46) Two friends started walking simultaneously from points A and B towards each other. 144 minutes later the distance between them was 20% of the original distance. After how much time they meet each other?

47) A dog finds a cat a 25 leaps away. The cat sees the dog coming towards it and starts running with the dog in hot pursuit. In every minute, the dog makes 5 leaps and the cat makes 6 leaps and one lap of the dog is equal to 2 leaps of the cat. Find the time in which the dog will catch the cat.

47) A thief steals car at 1.30 pm and drives it at 45 kmph. The theft is discovered at 2 pm and the owner sets off in another car at 50 kmph. He will overtake the thief at

48) Hari and Ravi started a race from opposite ends of the pool. After a minute and a half, they passed each other in the centre of the pool. If they lost no time in turning and maintained their respective speeds, how many minutes after starting did they pass each other second time?

49) Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in the train approaching the place hears the second shot 10 minutes after the first. The speed of the (in kmph), supposing that sound travels at 330 metres per second

50) The Taxi charges in a city contain fixed charges and additional charge per km. The fixed charge is for a distance of upto 5 km and additional charge per km thereafter. The charge for a distance of 10 km is 350/- and for 25 km is 800/-. The charge for a distance of 30 km is

51) A train after travelling 60 ľ km meets with an accident and then proceeds at áof its former speed and arrives at its destination 40 ľ minutes late. If the accident could have occurred 20 ľ km ahead, it would have reached the destination 10 ľ minute earlier. Find the speed of the train

52) The Speeds of three Cars are in the ratio 3 : 4 : 5. The time taken by each of them to travel the same distance is in the ratio is

53) The auto rickshaw fare consists of a fixed charge together with the charge for the distance covered. For a journey of 10 ľ km, the charge paid is 85/- and for a journey of 15 ľ km, the charge paid is 120/-. The fare for a journey of 25 ľ km will be

54) A Railway passenger counts the telegraph poles on the rail road as the passes them. The telegraph poles are at a distance of 50 m. What will be his count in 4 ľ hours if the speed of the train is 45 kmph ůůůůů

55) An aeroplane first flew with a speed of 440 kmph and covered a certain distance. It still had to cover 770 km less than what it had already covered but it flew with a speed of 660 kmph. The average speed for the entire flight was 500 kmph. Find the total distance covered

Solutions for Practice Problems will be available on Fdaytalk Quantitative Aptitude Book, Download Here