## PROBLEMS ON TRAINS – Aptitude Interview Questions with Answers

### This blog explains about PROBLEMS ON TRAINS – Aptitude Interview Questions with Answers and is given below :

1 . A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
 A 120 metres B 180 metres C 324 metres D 150 metres

Explanation:

 Speed= 60 x 5 m/sec = 50 m/sec. 18 3

Length of the train = (Speed x Time).

 Length of the train = 50 x 9 m = 150 m. 3

2 .The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
 A 200 m B 225 m C 245 m D 250 m

Explanation:

 Speed = 45 x 5 m/sec = 25 m/sec. 18 2

Time = 30 sec.

Let the length of bridge be x metres.

 Then, 130 + x = 25 30 2

2(130 + x) = 750

x = 245 m.

3 . Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
 A 1 : 3 B 3 : 2 C 3 : 4 D None of these

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

 27x + 17y = 23 x+ y

27x + 17y = 23x + 23y

4x = 6y

 x = 3 . y 2

4 .Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
 A 50 m B 72 m C 80 m D 82 m

Explanation:

Let the length of each train be x metres.

Then, distance covered = 2x metres.

Relative speed = (46 – 36) km/hr

 = 10 x 5 m/sec 18

 = 25 m/sec 9

 2x = 25 36 9

2x = 100

x = 50.

5 .Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
 A 9 B 9.6 C 10 D 10.8

Explanation:

 Relative speed = (60 + 40) km/hr = 100 x 5 m/sec = 250 m/sec. 18 9

Distance covered in crossing each other = (140 + 160) m = 300 m.

 Required time = 300 x 9 sec = 54 sec = 10.8 sec. 250 5

6 .A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
 A 130 B 360 C 500 D 540

Explanation:

 Speed = 78 x 5 m/sec = 65 m/sec. 18 3

Time = 1 minute = 60 seconds.

Let the length of the tunnel be x metres.

 Then, 800 + x = 65 60 3

3(800 + x) = 3900

x = 500.

7. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
 A 50 m B 150 m C 200 m D Data inadequate

Explanation:

Let the length of the train be x metres and its speed by y m/sec.

 Then, x = 15          y = x . y 15

 x + 100 = x 25 15

15(x + 100) = 25x

15x + 1500 = 25x

1500 = 10x

x = 150 m

8 .Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
 A 10 B 12 C 15 D 20

Explanation:

 Speed of the first train = 120 m/sec = 12 m/sec. 10

 Speed of the second train = 120 m/sec = 8 m/sec. 15

Relative speed = (12 + 8) = 20 m/sec.

 Required time = (120 + 120) sec = 12 sec. 20

9 . A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
 A 66 km/hr B 72 km/hr C 78 km/hr D 81 km/hr

Explanation:

 4.5 km/hr = 4.5 x 5 m/sec = 5 m/sec = 1.25 m/sec, and 18 4

 5.4 km/hr = 5.4 x 5 m/sec = 3 m/sec = 1.5 m/sec. 18 2

Let the speed of the train be x m/sec.

Then, (x – 1.25) x 8.4 = (x – 1.5) x 8.5

8.4x – 10.5 = 8.5x – 12.75

0.1x = 2.25

x = 22.5

 Speed of the train = 22.5 x 18 km/hr = 81 km/hr. 5

10 . A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
 A 230 m B 240 m C 260 m D 320 m E None of these

Explanation:

Relative speed = (120 + 80) km/hr

 = 200 x 5 m/sec 18

 = 500 m/sec. 9

Let the length of the other train be x metres.

 Then, x + 270 = 500 9 9

x + 270 = 500

x = 230.

11 . A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
 A. 230 m B. 240 m C. 260 m D. 270 m

Explanation:

 Speed = 72 x 5 m/sec = 20 m/sec. 18

Time = 26 sec.

Let the length of the train be x metres.

 Then, x + 250 = 20 26

x + 250 = 520

x = 270.

11 .Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
 A 2 : 3 B 4 : 3 C 6 : 7 D 9 : 16

Explanation:

Let us name the trains as A and B. Then,

(A’s speed) : (B’s speed) = b : a = 16 : 9 = 4 : 3.

12 .Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
 A 9 a.m. B 10 a.m. C 10.30 a.m. D 11 a.m.

Explanation:

Suppose they meet x hours after 7 a.m.

Distance covered by A in x hours = 20x km.

Distance covered by B in (x – 1) hours = 25(x – 1) km.

20x + 25(x – 1) = 110

45x = 135

x = 3.

So, they meet at 10 a.m.

13 .A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
 A 400 m B 450 m C 560 m D 600 m

Explanation:

Let the length of the first train be x metres.

 Then, the length of the second train is x metres. 2

 Relative speed = (48 + 42) kmph = 90 x 5 m/sec = 25 m/sec. 18

 [x + (x/2)] = 12 or 3x = 300     or     x = 200. 25 2

Length of first train = 200 m.

Let the length of platform be y metres.

 Speed of the first train = 48 x 5 m/sec = 40 m/sec. 18 3

 (200 + y) x 3 = 45 40

600 + 3y = 1800

y = 400 m.

14 . How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

 A 25 B 30 C 40 D 45

Explanation:

Speed of the train relative to man = (63 – 3) km/hr
= 60 km/hr

 = 60 x 5 m/sec 18

 = 50 m/sec. 3
Time taken to pass the man
 = 500 x 3 sec 50
= 30 sec.

15 . Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
 A 10 B 18 C 36 D 72

Explanation:

Let the speed of each train be x m/sec.

Then, relative speed of the two trains = 2x m/sec.

 So, 2x = (120 + 120) 12

2x = 20

x = 10.

 Speed of each train = 10 m/sec = 10 x 18 km/hr = 36 km/hr. 5