Question 1

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

Accepted Answer

Relative speed = (40 - 20) km/hr = ❨ 20 x 5 ❩ m/sec = ❨ 50 ❩ m/sec. 18 9 ∴ Length of faster train = ❨ 50 x 5 ❩ m = 250 m = 27 7 m. 9 9 9

Question 2

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 3

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 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:

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 5

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 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 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 8

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 9

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 10

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

Accepted Answer

Relative speed = (40 - 20) km/hr = ❨ 20 x 5 ❩ m/sec = ❨ 50 ❩ m/sec. 18 9 ∴ Length of faster train = ❨ 50 x 5 ❩ m = 250 m = 27 7 m. 9 9 9

Question 11

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 12

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.

Question 13

Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

Accepted Answer

Relative speed = (60+ 90) km/hr = ❨ 150 x 5 ❩m/sec 18 = ❨ 125 ❩m/sec. 3 Distance covered = (1.10 + 0.9) km = 2 km = 2000 m. Required time = ❨ 2000 x 3 ❩sec = 48 sec. 125

Question 14

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 15

A 270 meter 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 16

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 17

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 ar…

Accepted Answer

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

Question 18

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 19

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 20

A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

Accepted Answer

Speed = ❨ 300 ❩ m/sec = 50 m/sec. 18 3 Let the length of the platform be x metres. Then, ❨ x + 300 ❩ = 50 39 3 ⟹ 3(x + 300) = 1950 ⟹ x = 350 m.

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