Question 1

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 2

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 3

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 4

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 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.

Question 5

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 6

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

Accepted Answer

Let the length of the train be x metres and its speed by y m/sec. Then, x = 8 ⟹ x = 8y y Now, x + 264 = y 20 ⟹ 8y + 264 = 20y ⟹ y = 22. ∴ Speed = 22 m/sec = ❨ 22 x 18 ❩ km/hr = 79.2 km/hr. 5

Question 7

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?

Accepted Answer

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.

Question 8

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 9

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 10

A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

Accepted Answer

Total distance covered = ❨ 7 + 1 ❩ miles 2 4 = 15 miles. 4 ∴ Time taken = ❨ 15 ❩ hrs 4 x 75 = 1 hrs 20 = ❨ 1 x 60 ❩ min. 20 = 3 min.

Question 11

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 12

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 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

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 15

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 16

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?

Accepted Answer

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.

Question 17

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 18

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 19

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

Accepted Answer

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.

Question 20

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:

Accepted Answer

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

Problems on Trains Questions