TRAINS This chapter is basically an extension of the Time

and Distance". Therefore, we will use here the basic concepts like Speed, Relative Speed already discussed in the earlier chapter. Here, the focus will be exclu­sively on problems related to trains. The variables in­volved are again the same—Time, Distance and Speed.

Assumptions : For all purposes, unless otherwise specifically mentioned, we will assume that the speed at which the train(s) covers the distance or performs the journey remains constant over the journey which we call the average speed. The size of the person, tele­graph post, pole etc. is negligible in comparison to the length of the train or the platform. Important General Cases :

(0 Time ft) taken by a train x metres long to cross a stationary person or pole or signal post is equal to the time taken by the train to cover the distance x metres (equal to its own length) with its own speed (u).

Quantitative Aptitude

QUESTIONS FOR PRACTICE

1. A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 km/hr in 33 seconds. The speed of the train is ( l )30km/h (2)32km/h

2. Two trains started at the same time, one from A to B and the other from B to A. If they arrived at B and A respectively 4 hours and 9 hours after they passed each other, the ratio of the speeds of the two trains was (1 )2 :1 ( 2 ) 3 : 2 (3) 4 : 3 (4) 5 : 4

3. Two trains of equal length, running in opposite directions, pass a pole in 18 and 12 seconds. The trains will cross each other in (1) 14.4 seconds (2) 15.5 seconds (3) 18.8 seconds (4) 20.2 seconds

4. A moving train crosses a man standing on a plat­form and a bridge 300 metres long in 10 seconds and 25 seconds respectively. What will be the time taken by the train to cross a platform 200 metres long?

2

(1) 16— seconds (2) 18 seconds

(3) 20 seconds (4) 22 seconds 5. A train covers a distance of 3584 km in 2 days 8

hours. If it covers 1440 km on the first day and 1608 km on the second day, by how much does the average speed of the train for the remaining part of the journey differ from that for the entire journey ? (1) 3 km/hour more (2) 3 km/hour less (3) 4 km/hour more (4) 5 km/hour less

6. A train, 150m long, passes a pole in 15 seconds and another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train is (l)45km./hr (2)48km./hr (3) 52 km./hr (4) 54 km./hr

7. A train travelling at 48 km/hr crosses another train, having half its length and travelling in op­posite direction at 42 km/hr, in 12 seconds. It

also passes a railway platform in 45 seconds. The length of the railway platform is ( l )200m (2) 300m (3) 350 m (4) 400 m

8. Two trains 105 metres and 90 metres long, run at the speeds of 45 km/hr and 72 km/hr respec­tively, in opposite directions on parallel tracks. The time which they take to cross each other, is (1)8 seconds (2) 6 seconds (3) 7 seconds (4) 5 seconds

9. A train travelling at a speed of 30 m/sec crosses a platform, 600 metres long, in 30 seconds. The length (in metres) of train is (1) 120 (2) 150 (3) 200 (4) 300

10. A train passes a platform 110 m long in 40 sec­onds and a boy standing on the platform in 30 seconds . The length of the train is ( l) lOOm (2) 110 m (3) 220 m (4) 330 m

11. A train with a uniform speed passes a platform, 122 metres long, in 17 seconds and a bridge, 210 metres long, in 25 seconds. The speed of the train is (1) 46.5 km/hour (2) 37.5 km/hour (3) 37.6 km/hour (4) 39.6 km/hour

12. A train passes a platform 90 metre long in 30 seconds and a man standing on the platform in 15 seconds. The speed of the train is : (l)12.4kmph (2) 14.6kmph (3) 18.4 kmph (4) 21.6 kmph

13. A train passes two persons walking in the same direction at a speed of 3 km/hour and 5km/hour respectively in 10 seconds and 11 seconds respec­tively. The speed of the train is (1)28 km/hour (2) 27 km/hour (3) 25 km/hour (4) 24 km/hour

14. A 360 metre long train crosses a signal post in 18 seconds. What is the speed of the train in km per hour? (1) 76 (2) 60 (3) 64 (4) 72

15. A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is : ( l ) 8 0 m (2) 90 m (3) 200 m (4) 150 m

16. A train 300 metres long is running at a speed of 25 metres per second. It will cross a bridge of 200 metres in (1) 5 seconds (2) 10 seconds (3) 20 seconds (4) 25 seconds

17. A train is 125 m long. If the train takes 30 sec­onds to cross a tree by the railway line, then the speed of the train is (1)14 km/hr (2) 15 km/hr (3) 16 km/hr (4) 12 km/hr

18. A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is ( l ) 8 0 m (2) 90 m (3) 200 m (4) 150 m

19. A train takes 3 hours to run from one station to another. If it reduces its speed by 12 km/hr, it takes 45 minutes more for the journey. The dis­tance between the stations is (1)220 km (2) 210 km (3) 180 km (4) 160 km

20. The length of a train and that of a platform are equal. If with a speed of 90 km/hr the train crosses the platform in one minute, then the length of the train (in metres) is (1) 500 (2) 600 (3) 750 (4) 900

21. A train travelling with a speed of 60 km/hr catches another train travelling in the same direction and then leaves it 120 m behind in 18 seconds. The speed of the second train is (1) 26 km/hr (2) 35 km/hr (3) 36 km/hr (4) 63 km/hr

22. Two stations X and Y are 900km apart. A train starts from X and moves towards Y at 70 km/hr. Another train starts from Y at the same time and moves towards X at 80 km/hr. How far from X will they cross each other ? (1)150 km (2) 300 km (3) 420 km (4) 450 km

23. A train with a uniform speed crosses a pole in 2 seconds and a bridge of length 250m in 7 sec­onds. The length of the train is (1) 150 m (2) 120 m (3) 100 m (4) 80 m

24. A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 km/hr in 33 seconds. The speed of the train is (1)30 km/h (2) 32 km/h

25. A train. 240 m long crosses a man walking along the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed-of the train is (1)63 kmph (2) 75 kmph (3) 83.4 kmph (4) 86.4 kmph

ANSWERS

1.(4) 2. (2) 3.(1) 4. (3) 5.(1)

6. (4) 7. (4) 8. (2) 9. (4) 10. (4)

11.(4) 12. (4) 13. (3) 14. (4) 15. (3)

16. (3) 17. (2) 18. (3) 19. (3) 20. (3) 21. (3) 22. (3) 23. (3) 24. (4) 25. (3)