Problems on Trains

11.	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 Answer & Explanation Answer: Option A 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.

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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?
	A. 230 m B. 240 m C. 260 m D. 270 m Answer & Explanation Answer: Option D 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.

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13.	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:
	A. 30 km/hr B. 45 km/hr C. 60 km/hr D. 75 km/hr Answer & Explanation Answer: Option C Explanation: 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.

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14.	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 Answer & Explanation Answer: Option D 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

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15.	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?
	A. 5 sec B. 6 sec C. 7 sec D. 10 sec Answer & Explanation Answer: Option B Explanation: 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

16.	A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is 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?
	A. 2.5 min B. 3 min C. 3.2 min D. 3.5 min Answer & Explanation Answer: Option B Explanation: 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.

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17.	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 Answer & Explanation Answer: Option C 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.

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18.	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?
	A. 320 m B. 350 m C. 650 m D. Data inadequate Answer & Explanation Answer: Option B Explanation: 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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19.	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 Answer & Explanation Answer: Option B 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.

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20.	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?
	A. 69.5 km/hr B. 70 km/hr C. 79 km/hr D. 79.2 km/hr Answer & Explanation Answer: Option D Explanation: 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

21.	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 Answer & Explanation Answer: Option B 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.

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22.

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.

A. 12 sec B. 24 sec C. 48 sec D. 60 sec Answer & Explanation Answer: Option B Explanation: 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

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23.	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 Answer & Explanation Answer: Option C 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

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24.	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 Answer & Explanation Answer: Option B 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

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25.	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:
	A. 48 km/hr B. 54 km/hr C. 66 km/hr D. 82 km/hr Answer & Explanation Answer: Option D Explanation: 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.

26.	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?
	A. 23 m B. 23 2 m 9 C. 27 7 m 9 D. 29 m Answer & Explanation Answer: Option C Explanation: 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

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27.	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:
	A. 45 m B. 50 m C. 54 m D. 72 m Answer & Explanation Answer: Option B Explanation: 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.

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28.	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 Answer & Explanation Answer: Option D 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

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29.

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 Answer & Explanation Answer: Option A 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.

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30.	Two stations A and B are 110 km apart on a staright 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. Answer & Explanation Answer: Option B 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.