Question 1

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 2

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 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

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 5

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

Question 6

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 7

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:

Accepted Answer

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

Question 8

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 9

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 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 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 12

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 13

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 14

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 15

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 16

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

Question 17

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 18

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 19

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.

Question 20

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.

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