1. A speed of 14 meters per second is the same as :
Explanation: 14 m / sec = (14 x 18/5) km / hr = 50.4 km/hr
2. A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line.
Explanation: Speed of train = (30 x 5/18) m / sec = (25/3) m/ sec
Distance moved in passing the standing man = 100 m
Required time taken = 100/(25/3) = (100 x (3/25)) sec => 12 sec
3. A train 150 m long is running with a speed of 68 kmph. In what time will it pass a men who is running at 8 kmph in the same direction in which the train is it pass a man who is running at 8 kmph in the same direction in which the train is going?
Explanation: Speed of train relative to man = (68 - 8) kmph =(60 x (5/18))m /sec = 50/3 m / sec
Time taken by the train to cross the man
=Time taken by it to cover 150 m at (50/3) m / sec
=> (150 x (3/50)) sec = 9 sec
4. A train 150 m long is running with a speed of 68 kmph. In what time will it pass a men who is running at 8 kmph in the same direction in which the train is it pass a man who is running at 8 kmph in the same direction in which the train is going?
Explanation: Speed of train = (132 x 5 / 18)m / sec = (110/3)m / sec
Distance covered in passing the platform = (110 + 165) m = 275 m
Time taken = (275 x (3/110)) sec = 15/2 sec
5. A train moves with a speed of 108 kmph. its speed in meters per second is :
Explanation: 108 km / hr = (108 x (5 / 18) m / sec = 30 m / sec
6.A man sitting in a train which is travelling at 50 km / hr observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. if the goods train is 280 m long, find its speed.
Explanation: Relative speed = (280/9)m / sec
= [(280/9) x(18/5)] km / hr = 112 km/ hr
Speed of goods train = (112 - 50) km / hr = 62 km / hr.
7.In What time will a train 100 meters long cross an electric pole, if its speed be 144 km / hr?
Explanation: Speed = (144 x (5/18)) m / sec = 40 m / sec
Time taken = (100/40) sec = 2.5 sec.
8.Two trains 100 meters and 120 meters long are running in the same direction with speed of 72 km / hr and 54 km / hr. In how much time will the first train cross the second?
Explanation: Relative speed of trains = (72 - 54) km / hr = 18 km / hr
=(18 x (5/18)) m / sec = 5 m / sec
Time taken by the trains to cross each other
= Time taken to cover (100 + 120) m at 5 m / sec = (220/5) sec = 44 sec.
9.A train 200 m long, running with a speed of 63 km / hr will pass a tree in :
Explanation: Speed = (63 x (5 / 18)) m / sec = 35/2 m / sec
Time taken = (280 x (2/35)) sec = 16 sec .
10. A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
Explanation: Let the length of the train be x meters
Then the train covers x meters in 8 sec and ( x + 180) meters in 20 seconds .
x/8 = (x + 180)/20 <=> 20 x = 8(x + 180) = x = 120
Length of the train = 120 m Speed of train = (120/8) m / sec = 15 m / sec
= (15 x (18/5)) km / hr = 54 km / hr.
11.How long does a train 110 meters long running at the speed of 72 km / hr take to cross a bridge 132 meters in length?
Explanation: Speed = (72 x (5 / 18) m / sec = 20 m / sec
Total distance covered = (110 + 132)m = 242 m
Required time = (242 / 20) sec = 12.1 sec.
12.A train 100 meters long takes 6 sec to cross a man walking at 5 km / hr in a direction opposite to that of the train. Find the speed of the train.
Explanation: Let the speed of the train be x km / hr.
Speed of the train relative to man = (x + 5) km / hr
= (x + 5) x (5/18) m / sec 100/(x + 5) x (5/18) = 6 <=> 30(x + 5) = 1800 <=> x = 55.
Speed of the train is 55 km / hr.
13.A train 360 m long is running at the speed of 45 km / hr. In what time will it pass a bridge 140 m long?
Explanation: Speed = (45 x (5/18)) m / sec = 25/2 m / sec
Total distance covered = (360 + 140)m = 500 m
Required time = (500 x (2/25)) sec = 40 sec.
14.A train is travelling at the speed 75 m / hr enters atunnel 7 / 2 miles long. The train is 1/4 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?
Explanation: Total distance covered = (7/2 + 1/4) miles = 15/4 miles
Time taken = (15/(4 x 75)) hrs = 1/20 hrs = (1/20 x 60) min = 3 min.
15.A train 360 m long is running at speed of 60 km / hr crosses a poles in 9 seconds . What is the length of the train?
Explanation: Speed = (60 x 5/18) m / sec = (50/3)m/sec
Length of the train = (speed x time) = (50/3 x 9)m = 150 m.
16.A train 132 m long passes a telegraph pole in 6 sec. Find the speed of train?
Explanation: Speed = (132/6) m / sec = (22 x 18 / 5)km / hr = 79.2 km / hr.
17.A train covers a distance of 12 km in 10 minutes. if it takes 6 sec to pass a telegraph post then the length of the train is:
Explanation: Speed = (12/10 x 60) km / hr = (72 x 5/18) m / sec = 20 m / sec
Length of the train = (speed x time) = (20 x 6) = 120 m.
18.A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Explanation: Speed = (240/24) m / sec = 10 m / sec
Required time = (240 + 650)/10 sec = 89 sec.
19.The length of the bridge which a train 130 m long and travelling at 45 km / hr can cross in 30 sec, is
Explanation: Speed = (45 x 5/18) m / sec = 25/2 m / sec , time = 30 sec
Let the length of the bridge be x meters.
then (130 + x)/30 = 25/2 = 2(130 + x) = 750 <=> x = 245 m.
20.A train 800 m long is running at the speed of 78 km / hr. If it crosses a tunnel in 1 minutes then the length of the tunnel in 1 minute, then the length of the tunnel is:
Explanation: Speed = (78 x 5/18) m / sec = (65/3)m/sec Time = 1 minutes = 60 sec
Let the length of the tunnel be x meters
then, (800 + x)/60 = 65/3 = 3(800 + x) = 3900 <=> x = 500 m.
21. A train speed past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Explanation: Let the length of the train be x meters and
its speed be y m / sec/ Then, x/y = 15 => y =>x/15
(x + 100)/25 = x/15 => x = 150 m.
22.Two trains are running in opposite directions with the same speed. if the length of each train is 120 m and they cross each other in 12 sec. then the speed of each train is :
Explanation: Let the speed of each train be x m / sec.
then relative speed of the two trains = 2 x m / sec.
So, 2 x = (120 + 120)/ 12 = > 2 x = 20 =>x = 10.
Speed of each train = 10 m / sec = (10 x 18/5) km / hr = 36 km / hr.
23.Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 km / hr and 45 km / hr respectively. In how much time will they cross each other, if they are running in the same direction?
Explanation: Relative speed = (45 - 40) km / hr = 5 km / hr = (5 x 5/18) m / sec = 25/18 m / sec
Total distance covered = Sum of lengths of trains = 350 m.
Time taken = (350 x 18/25) sec = 252 sec.
24.A train crosses a platform 100 m long in 60 sec at the speed of 45 km /hr . The time taken by the train to cross an electric pole is :
Explanation: Speed = (45 x 5/18) m / sec = 25/2 m / sec
Let the length of the train be x meters.
Then, (x + 100)/25/2 = 60 or x = 650 m.
Time taken by the train to cross an electric pole = (650 x 2/25) sec = 52 sec.
25.A train 110 m long passes a man, running at 16 km / hr in the direction opposite to that of the train, in 6 sec. the speed of the train is .
Explanation: Speed of the train relative to man = (110/6)m/sec = (110/6 x 18/5) km / hr = 66 km / hr. Let the speed of the train be x km / hr.
Then relative speed = (x + 6) km / hr.
x + 6 = 66 or x = 60 km / hr.
26.A train moves past a telegraph post and bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Explanation: Let the length of the train be x meters and
its speed be y m / sec.
Then, x/y = 8 => x = 8 y
Now, (x + 264)/20 = y => 8 y + 264 = 20 y <=> y = 22
Speed = 22 m / sec = (22 x 18 / 5) km / hr = 79.2 km / hr.
27.The length of a train an that of a platform are equal. If with a speed of 90 km /hr , the train crosses the platform in one minutes, then the length of the train is.
Explanation: Speed = (90 x 5/18) m / sec = 25 m / sec, Time = 1 min = 60 sec
Let the length of the train and that of the platform be x meters.
Then, 2 x/ 60 = 25 <=> x = (25 x 60)/2 = 750 m.
28.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.
Explanation: Let us name the trains as A and B
Then, (A's speed) : (B's speed) = root b : root a = 4 : 3
29.A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 km / hr and 4 km / hr and passes them completely in 9 and 10 sec respectively. The length of the train is.
Explanation: 2 km / hr = (2 x 5/18)m /sec = 5/9 m/sec and 4 km / hr = 10/9 m / sec.
Let the length of the train be x meters and its speed be y m / sec.
Then, x/(y - 5/9) = 9 and x/(y - 10/9) = 10 , 9 y - 5 = x and
10(9 y - 10) = 9 x = 9 y - x = 5 and 90 y - 9 x = 100
on solving, we get : x = 50 Length of the train is 50 m.
30.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?
Explanation: Speed of the the train relative to man = (63 - 3) km / hr = 60 km / hr.
=(60 x 5/18) m / sec = 50/3 m / sec.
Time taken to pass the man = (500 x (3/50)) sec = 30 sec.
31.A train of length 150 m takes 40.5 sec to cross a tunnel of length 300 metres. What is the speed of the train in km / hr?
Explanation: Speed = (150 + 300)/40.5 m / sec = (450/40. 5 x 18/5) km / hr = 40 km / hr.
32.A 270 metres long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec What is the length of the other train?
Explanation: Relative speed = (120 + 80) km / hr = (200 x 5/18) m / sec = (500/9) m / sec.
Let the length of the other train be x meters.
Then, (x + 270)/9 = 500/9 = x + 270 = 500 <=> x = 230 m.
33.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 km / hr. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 km / hr. At what time will they meet?
Explanation: Suppose they meet x hours after 7 a. m distance covered by A in x hours = 20 x km Distance covered by B in (x - 1) hours = 25(x - 1)km 20 x + 25(x - 1) = 110 = 45 x = 135 <=> x = 3 So,they meet at 10 a.m.
34.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.
Explanation: Relative speed = (60 + 90) km / hr =(150 x 5/18) m / sec = (125/3)m / sec.
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = (2000 x 3/125) sec = 48 sec.
35.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?
Explanation: 4.5 km / hr = (4.5 x 5/ 18) m / sec = 5/ 4 m / sec = 1.25 m / sec and,
5.4 km / hr = (5.4 x 5/18) m / sec = 3/2 m / sec = 1.5 m / sec
Let the speed of the train be x m / sec.
Then, (x - 1.25) x 84 = (x - 1.5) x 8.5
84 x - 10.5 = 8.5 x - 12.75 <=> 0.1 x => 2.25 <= >x = 22.5
Speed of the train = (22.5 x 18/5) km / hr = 81 km / hr.
36.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.
Explanation: Let the length of each train be x metres.
Then, distance covered = 2 x metres.
Relative speed = (46 - 36) km / hr = (10 x 5/18) m / sec = (25/9) m / sec.
2 x / 36 = 25 /9 = 2 x = 100 => x = 50 m.
37.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 will they cross each other travelling in opposite direction?
Explanation: Speed of first train = (120/10) m / sec = 12 m / sec.
Speed of the second train = (120/15) m / sec = 8 m / sec.
Relative speed = (12 + 8) m / sec = 20 m / sec.
Required time = (120 + 120)/20 = 12 sec.
38.A train 110 m long is running with the speed of 60 km / hr. In what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going?
Explanation: Speed of train relative to man = (60 + 6) km / hr = 66 km / hr.
=(66 x 5 /18) m / sec = (55/3)m/sec.
Time taken to pass the man = (110 x 3/55) sec = 6 sec.
39.Two trains travel in opposite directions at 36 km / hr and 45 km / hr and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is.
Explanation: Relative speed = (36 + 45) km / hr = (81 x 5/18) m / sec = (45/2)m / sec.
Length of train = (45/2 x 8) m = 180 m.
40.A train 125 m long passes a man, running running at 5 km / hr in the same direction in which the train is going, in 10 seconds. The speed of train is.
Explanation: Speed of the train relative to man = (125/10) m / sec = (25/2) m/sec.
=(25/2 x 18/5) km / hr = 45 km / hr.
Let the speed of the train be x km / hr
then relative speed = (x - 5) km / hr. x - 5 = 45 or x = 50 km / hr.
41.A train 108 m long moving at 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.
Explanation: Let the speed of the second train be x km / hr.
Relative speed = (x + 50) km / hr = [(x + 50) x 5/18] m / sec = (250 + 5 x)/18 m/sec.
Distance covered = (108 + 112) = 220 m.
220/[(250 + 5 x)/18] = 6 <=> 250 + 5 x = 660 <=> x = 82 km / hr.
42.A train travelling at 48 km / hr completely crosses another train having half its length and travelling in opposite direction at 42 km /hr, in 12 seconds. It also passes a railway platform in 45 seconds. The length of platform is.
Explanation: Let the length of first train be x metres.
Then, the length of second train is (x/2) metres.
Relative speed = (48 + 42) km / hr = (90 x 5/18) m / sec = 25 m / sec.
(x + x/2)/25 = 12 or 3 x / 2 = 300 or x = 200.
Length of first train = 200 m.
Let the length of the platform be y metres.
Speed of the first train = (48 x 5 / 18) m / sec = 40/ 3 m / sec.
(200 + y) x 3/40 = 45 <=> 600 + 3 y = 1800 <=> y = 400 m.
43.A 300 metres long train crosses a platform in 39 sec while it crosses a signal pole in 18 seconds. What is the length of the platform?
Explanation: Speed = (300/18) m/sec = (50 /3) m/sec.
Let the length of the platform be x metres.
Then, (x + 300)/39 = 50/3 <=> 3(x + 300) = 1950 <=> x = 350 m.
44.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 the slower train in 5 seconds. What is the length of the fast train?
Explanation: Relative speed = (40 - 20) km / hr = (20 x 5/18) m / sec = (50/9)m/sec.
Length of the faster train = (50/9 x 5) m = 250/9 m.
45.Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hrrespectively in opposite directions on parallel tracks. The time which they take to cross each other, is.
Explanation: Relative speed = (60 + 40)km/hr = (100 x 5/18) m/sec = (250/9)m/sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = (300 x 9/250)sec = 54/5 sec = 10.8 sec.
46. 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.
Explanation: Let the speed of two trains be x m / sec and y m/sec respectively.
Then, length of the first train = 27 x metres, and l
ength of the second train = 17 y metres.
(27 x + 17 y) / (x + y) = 23 <==> 27 x + 17 y = 23 x + 23 y => 4 x = 6 y => x : y = 3 : 2.
47.A train 150 m long passes a km stone in 15 sec and another train of the same length travelling in opposite direction in 8 seconds. The speed of second train is.
Explanation: Speed of first train = (150/15) m / sec = 10 m / sec.
Let the speed of the second train be x m / sec.
Relative speed = (10 + x) m / sec. 300/(10 + x) = 8 <=> 300 = 80 + 8 x <=> x = 220/8 = (55/2) m/sec. So speed of second train = (55/2 x 18/5) km / hr = 99 km /hr.
48.Two goods train each 500m 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.
Explanation: Relative speed =(45 + 30) km / hr = (75 x 5/18)m/sec = (125/6)m/sec.
Distance covered = (500 + 500)m = 1000 m.
Required time = (1000 x 6/125) sec = 48 sec.
49.A jogger running at 9 km/hr alongside a railway track is 240 meters ahead of the engine of 120 metres long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Explanation: Speed of train relative to jogger = (45 - 9) km / hr = 36 km /hr.
(36 x 5/18)m/sec = 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
Time taken = (360/10)sec = 36 sec.
50.A train passes a station platform in 36 sec 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?
Explanation: Speed = (54 x 5/18)m/sec = 15 m/sec.
Length of the train = (15 x 20) m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/36 = 15 <=> x + 300 = 540
x => 240 m.