Question 1

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

Accepted Answer

Let the speed of the second train be x km/hr. Relative speed = (x + 50) km/hr = [ (x + 50) x 5 ] m/sec 18 = [ 250 + 5x ] m/sec. 18 Distance covered = (108 + 112) = 220 m. ∴ 220 = 6 ❨ 250 + 5x ❩ 18 ⟹ 250 + 5x = 660 ⟹ x = 82 km/hr.

Question 2

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

Accepted Answer

Let the length of the first train be x meters. Then, the length of the second train is ❨ x ❩ meters. 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 meters. 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.

Question 3

Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

Accepted Answer

Relative speed = = (45 + 30) km/hr = ❨ 75 x 5 ❩ m/sec 18 = ❨ 125 ❩ m/sec. 6 We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train. So, distance covered = Length of the slower train. Therefore, Distance covered = 500 m. ∴ Required time = ❨ 500 x 6 ❩ = 24 sec. 125

Question 4

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:

Accepted Answer

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

Question 5

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

Accepted Answer

2 kmph = ❨ 2 x 5 ❩ m/sec = 5 m/sec. 18 9 4 kmph = ❨ 4 x 5 ❩ m/sec = 10 m/sec. 18 9 Let the length of the train be x metres and its speed by y m/sec. Then, ❨ x ❩ = 9 and ❨ x ❩ = 10. y - 5 9 y - 10 9 ∴ 9y - 5 = x and 10(9y - 10) = 9x ⟹ 9y - x = 5 and 90y - 9x = 100. On solving, we get: x = 50. ∴ Length of the train is 50 m.

Question 6

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

Accepted Answer

Let the speed of the slower train be x m/sec. Then, speed of the faster train = 2x m/sec. Relative speed = (x + 2x) m/sec = 3x m/sec. ∴ (100 + 100) = 3x 8 ⟹ 24x = 200 ⟹ x = 25 . 3 So, speed of the faster train = 50 m/sec 3 = ❨ 50 x 18 ❩km/hr 3 5 = 60 km/hr.

Question 7

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

Accepted Answer

Speed = ❨ 240 ❩m/sec = 10 m/sec. 24 ∴ Required time = ❨ 240 + 650 ❩sec = 89 sec. 10

Question 8

A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

Accepted Answer

Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr. = ❨ 36 x 5 ❩m/sec 18 = 10 m/sec. Distance to be covered = (240 + 120) m = 360 m.

Question 9

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?

Accepted Answer

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

Question 10

A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

Accepted Answer

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr. = ❨ 66 x 5 ❩m/sec 18 = ❨ 55 ❩m/sec. 3 ∴ Time taken to pass the man = ❨ 110 x 3 ❩sec = 6 sec. 55

Question 11

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

Accepted Answer

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.

Question 12

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?

Accepted Answer

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.

Question 13

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Accepted Answer

Speed = ❨ 54 x 5 ❩m/sec = 15 m/sec. 18 Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, x + 300 = 15 36 ⟹ x + 300 = 540 ⟹ x = 240 m.

Question 14

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:

Accepted Answer

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.

Question 15

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?

Accepted Answer

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.

Question 16

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Accepted Answer

Speed of the train relative to man = ❨ 125 ❩m/sec 10 = ❨ 25 ❩m/sec. 2 = ❨ 25 x 18 ❩km/hr 2 5 = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. ∴ x - 5 = 45 ⟹ x = 50 km/hr.

Question 17

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Accepted Answer

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

Question 18

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

Accepted Answer

Formula for converting from km/hr to m/s: X km/hr = ❨ X x 5 ❩ m/s. 18 Therefore, Speed = ❨ 45 x 5 ❩m/sec = 25 m/sec. 18 2 Total distance to be covered = (360 + 140) m = 500 m. Formula for finding Time = ❨ Distance ❩ Speed ∴ Required time = ❨ 500 x 2 ❩sec = 40 sec. 25

Question 19

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:

Accepted Answer

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.

Question 20

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:

Accepted Answer

Let us name the trains as A and B. Then, (A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

Problems on Trains Questions