Explanation / Important formulas:
 km/hr to m/s conversion: a km/hr = (a X 5/18) m/s
 m/s to km/hr conversion: a km/hr = (a X 18/5) km/hr
 Time taken by a train of length metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres
 Time taken by a train of length metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres
 Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u – v) m/s
 Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s
 If two trains of length metres and b metres are moving in opposite directions at u m/s and v m/s, then: their relative speed is = (u – v) m/s
 Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s
 If two trains of length metres and b metres are moving in opposite directions at u m/s and v m/s, then: The time taken by the trains to cross each other = (a+b) / (u+v) sec
 The time taken by the faster train to cross the slower train = (a+b) / (uv) sec
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Test  Problems on trains
Problems on trains  Question and Answers
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Question 1

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

Question 1 Explanation:
Let the speed of the second train be xkm/hr
Relative speed = (x + 50) km/hr
= [(x + 50) * 5 / 18] m/sec
=[(250 + 5x) / 18] m/sec
Distance covered = (108 + 112) = 220 m
Therefore, (250 + 5x) / 18 = 6
250 + 5x = 660 x = 82 km/hr
Relative speed = (x + 50) km/hr
= [(x + 50) * 5 / 18] m/sec
=[(250 + 5x) / 18] m/sec
Distance covered = (108 + 112) = 220 m
Therefore, (250 + 5x) / 18 = 6
250 + 5x = 660 x = 82 km/hr
Question 2

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

Question 2 Explanation:
Speed = (78 * 5/18) m/sec = 65/3 m/sec
Time = 1 minute = 60 seconds
Let the length of the tunnel be x metres
Then, (800 + x) / 60 = 65 / 3
3(800 + x) = 3900 x = 500
Time = 1 minute = 60 seconds
Let the length of the tunnel be x metres
Then, (800 + x) / 60 = 65 / 3
3(800 + x) = 3900 x = 500
Question 3

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?
A

50 m

B

72 m

C

80 m

D

82 m

Question 3 Explanation:
Let the length of each train be x metres
Then, distance covered = 2xmetres
Relative speed = (46  36) km/hr
= (10 * 5 / 18) m/sec
= (25 / 9) m/sec
Therefore,( 2x / 36) = (25 / 9)
2x = 100 x = 50
Then, distance covered = 2xmetres
Relative speed = (46  36) km/hr
= (10 * 5 / 18) m/sec
= (25 / 9) m/sec
Therefore,( 2x / 36) = (25 / 9)
2x = 100 x = 50
Question 4

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?
A

45 km/hr

B

50 km/hr

C

54 km/hr

D

55 km/hr

Question 4 Explanation:
Speed of the train relative to man = (125 / 10)
= (25/2) m/sec
= (25 / 2 * 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 => x = 50 km/hr
= (25/2) m/sec
= (25 / 2 * 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 => x = 50 km/hr
Question 5

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?
A

36

B

45

C

48

D

49

Question 5 Explanation:
Relative speed = (60+ 90) km/hr
=(150 * 5 / 18) m/sec
= (125 / 3) m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m
Required time = (2000 * (3/125) sec = 48 sec
=(150 * 5 / 18) m/sec
= (125 / 3) m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m
Required time = (2000 * (3/125) sec = 48 sec
Question 6

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

Question 6 Explanation:
Speed = (72 * 5 / 18) m/sec = 20 m/sec
Time = 26 sec
Let the length of the train be x metres
Then, (x + 250) / 26 = 20
x + 250 = 520 x = 270
Time = 26 sec
Let the length of the train be x metres
Then, (x + 250) / 26 = 20
x + 250 = 520 x = 270
Question 7

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?
A

9 a.m

B

10 a.m

C

10.30 a.m

D

11 a.m

Question 7 Explanation:
Suppose they meet x hours after 7 a.m
Distance covered by A in x hours = 20xkm
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
Distance covered by A in x hours = 20xkm
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 8

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

Question 8 Explanation:
Let the speed of each train be xm/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 * 18/5)km/hr = 36 km/hr
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 * 18/5)km/hr = 36 km/hr
Question 9

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?
A

40 sec

B

42 sec

C

45 sec

D

48 sec

Question 9 Explanation:
Formula for converting from km/hr to m/s: Xkm/hr = (X * 5 / 18) m/sec
Therefore, Speed = (45 * 5 /18) m/sec
= 25/2 m/sec
Total distance to be covered = (360 + 140) m = 500 m
Formula for finding Time = (Distance / Speed)
Required time = (500 x 2 / 25)sec = 40 sec
Therefore, Speed = (45 * 5 /18) m/sec
= 25/2 m/sec
Total distance to be covered = (360 + 140) m = 500 m
Formula for finding Time = (Distance / Speed)
Required time = (500 x 2 / 25)sec = 40 sec
Question 10

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A

200 m

B

225 m

C

245 m

D

250 m

Question 10 Explanation:
Speed = (45 x 5 / 18) m/sec = (25 / 2) m/sec
Time = 30 sec
Let the length of bidge be x metres
Then, (130 + x / 30) = 25 / 2
2(130 + x) = 750 x = 245 m
Time = 30 sec
Let the length of bidge be x metres
Then, (130 + x / 30) = 25 / 2
2(130 + x) = 750 x = 245 m
Question 11

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A

200 m

B

225 m

C

245 m

D

250 m

Question 11 Explanation:
Speed = (45 x 5 / 18) m/sec = (25 / 2) m/sec
Time = 30 sec
Let the length of bidge be x metres
Then, (130 + x / 30) = 25 / 2
2(130 + x) = 750 x = 245 m
Time = 30 sec
Let the length of bidge be x metres
Then, (130 + x / 30) = 25 / 2
2(130 + x) = 750 x = 245 m
Question 12

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
A

65 sec

B

89 sec

C

100 sec

D

150 sec

Question 12 Explanation:
Speed = (240 / 24) m/sec = 10 m/sec
Therefore, Required time = (240 + 650) / 10sec = 89 sec
Therefore, Required time = (240 + 650) / 10sec = 89 sec
Question 13

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?
A

39 sec

B

18 sec

C

36 sec

D

72 sec

Question 13 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
Therefore, time taken = 360 /10 sec = 36 sec
= (36 x (5 / 18)) m/sec
= 10 m/sec
Distance to be covered = (240 + 120) m = 360 m
Therefore, time taken = 360 /10 sec = 36 sec
Question 14

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

Question 14 Explanation:
Speed of the train relative to man = (63  3) km/hr
= 60 km/hr
= (60 * 5 / 18) m/sec
= (50 / 3) m/sec
Therefore, time taken to pass the man = (500 * 3/50 ) sec
= 30 sec
= 60 km/hr
= (60 * 5 / 18) m/sec
= (50 / 3) m/sec
Therefore, time taken to pass the man = (500 * 3/50 ) sec
= 30 sec
Question 15

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

Question 15 Explanation:
Let the speed of the slower train be xm/sec
Then, speed of the faster train = 2xm/sec
Relative speed = (x + 2x) m/sec = 3xm/sec
Hence (100 + 100) / 8 = 3x
24x = 200
x = 25 / 3
So, speed of the faster train = 50/3 m/sec
= (50 / 3) * (18 / 5) km/hr
= 60 km/hr
Then, speed of the faster train = 2xm/sec
Relative speed = (x + 2x) m/sec = 3xm/sec
Hence (100 + 100) / 8 = 3x
24x = 200
x = 25 / 3
So, speed of the faster train = 50/3 m/sec
= (50 / 3) * (18 / 5) km/hr
= 60 km/hr
Question 16

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?
A

120 m

B

240 m

C

300 m

D

None of these

Question 16 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
Question 17

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?
A

1 : 3

B

3 : 2

C

3 : 4

D

None of these

Question 17 Explanation:
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
Therefore, (27x + 17y) / (x + y) = 23
27x + 17y = 23x + 23y 4x = 6y
x/y = 3/2
Then, length of the first train = 27x metres, and length of the second train = 17y metres
Therefore, (27x + 17y) / (x + y) = 23
27x + 17y = 23x + 23y 4x = 6y
x/y = 3/2
Question 18

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 sec. What is the length of the fast train?
A

23 m

B

23 2/9 m

C

27 m

D

27 7/9 m

Question 18 Explanation:
Relative speed = (40  20) = 20 km/hr
= 20 * 5/18 = 50/9 m/sec
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m
= 20 * 5/18 = 50/9 m/sec
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m
Question 19

How many seconds will a 500 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train?
A

42

B

50

C

30

D

28

Question 19 Explanation:
Distance = 500 m
Speed of the train relative to man = ( 63  3 ) km/hr = 60 km/hr
= (60 x 5/18) m/s = 50/3 m/s
Time taken to pass the man = distance/speed = (500 x 3/50) sec = 30 sec
Speed of the train relative to man = ( 63  3 ) km/hr = 60 km/hr
= (60 x 5/18) m/s = 50/3 m/s
Time taken to pass the man = distance/speed = (500 x 3/50) sec = 30 sec
Question 20

Two trains leaving from two station 50 miles away from each other with costant speed of 60 miles per hour, approaches towards each other on diffrent tracks. if length of each train is 1/6 mile. When they meet how much time they need to pass each other totally?
A

1/6 minutes

B

1/4 minutes

C

1/8 minutes

D

1/2 minutes

Question 20 Explanation:
As we know ,Both are approaching each other relative speed = 60+60 = 120m/h
Distance = 50m(Given)
Time = 50/120 = 5/12 hrs = 25 minutes to meet Now,
Relative length of train = 1/6 + 1/6 = 1/3m
Relative speed = 120m/h
Rime to cross both the trains = ( 1/3 )/120 = 1/360 Hours
Convert it into minutes = 1/6 minutes
Distance = 50m(Given)
Time = 50/120 = 5/12 hrs = 25 minutes to meet Now,
Relative length of train = 1/6 + 1/6 = 1/3m
Relative speed = 120m/h
Rime to cross both the trains = ( 1/3 )/120 = 1/360 Hours
Convert it into minutes = 1/6 minutes
Question 21

The time a passenger train takes to cross another freight train is twice when the passenger train crosses the freight train running in opposite directions. What is the ratio of their speeds?
A

2:8

B

3:1

C

3:2

D

2:6

Question 21 Explanation:
Speed of freight train = x
Speed of passenger train = y
Sum of their length = s
So time = s/(x – y)when both are in same direction
Time = s/(x + y) when opposite direction
From question s/(x – y) = 2. s/(x + y) so solving this we get, x/y = 3/1
So x : y = 3 : 1
Speed of passenger train = y
Sum of their length = s
So time = s/(x – y)when both are in same direction
Time = s/(x + y) when opposite direction
From question s/(x – y) = 2. s/(x + y) so solving this we get, x/y = 3/1
So x : y = 3 : 1
Question 22

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?
A

9 a.m

B

10 a.m

C

10.30 a.m

D

11 a.m

Question 22 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
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 23

Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?
A

75m

B

80m

C

70m

D

86m

Question 23 Explanation:
Relative speed = (5032)
t = 15/(60 * 60) = time taken in hours
length = t*rs = 75m
t = 15/(60 * 60) = time taken in hours
length = t*rs = 75m
Question 24

Two trains of length 400 meters and 300 meters starts at 6.00 pm and 7.00 pm and runs at the speed of 80 km/hr and 90 km/hr respectively. If they are running on parallel tracks in the same direction then the time taken by them to cross each other is?
A

219 seconds

B

252 seconds

C

198 seconds

D

202 seconds

Question 24 Explanation:
Length of the two trains are 400 meters and 300 meters and their respective speeds are 80 km/hr and 90 km/hr
Since the trains are moving in the same direction,the time required to cross each other = (a + b)/(u  v) sec
Here, a = 300 m, b = 400 m and u = 90 km/hr, v = 80 km/hr
a + b = 300 + 400 = 700 m
And, u  v = (90  80)km/hr = 10 km/hr
Converting the unit of speed into m/Sec:
10 km/hr = 10 x 5/18 m/sec = 50/18 m/s
Now, the required time = 700 x 18/50 sec = 252 sec
Since the trains are moving in the same direction,the time required to cross each other = (a + b)/(u  v) sec
Here, a = 300 m, b = 400 m and u = 90 km/hr, v = 80 km/hr
a + b = 300 + 400 = 700 m
And, u  v = (90  80)km/hr = 10 km/hr
Converting the unit of speed into m/Sec:
10 km/hr = 10 x 5/18 m/sec = 50/18 m/s
Now, the required time = 700 x 18/50 sec = 252 sec
Question 25

Two trains of length 0.55 km and 0.45 km run at the rate of 30 km/hr and 45 km/hr. If they are travelling on parallel tracks in the opposite direction then how long will the slower train takes to cross the faster train?
A

48 seconds

B

52 seconds

C

39 seconds

D

98 seconds

Question 25 Explanation:
Length of the two trains are 0.55 km and 0.45 km and their respective speeds are 30 km/hr and 45 km/hr
Since the trains are moving in the opposite direction, the time required to cross each other = (a + b)/(u + v) sec
Here, a = 0.55 km = 550 meters, b = 0.45 km = 450 meters and u = 30 km/hr, v = 45 km/hr
a + b = 550 + 450 = 1000 m
And, u + v = (30 + 45)km/hr = 75 km/hr
Converting the unit of speed into m/Sec:
75 km/hr = 75 x 5/18 m/sec = 375/18 m/s
Now, the required time = 1000 x 18/375 sec = 48 sec
Since the trains are moving in the opposite direction, the time required to cross each other = (a + b)/(u + v) sec
Here, a = 0.55 km = 550 meters, b = 0.45 km = 450 meters and u = 30 km/hr, v = 45 km/hr
a + b = 550 + 450 = 1000 m
And, u + v = (30 + 45)km/hr = 75 km/hr
Converting the unit of speed into m/Sec:
75 km/hr = 75 x 5/18 m/sec = 375/18 m/s
Now, the required time = 1000 x 18/375 sec = 48 sec
Question 26

The speed ratio of two trains each of length 250 meters is same and are running on parallel tracks in the opposite direction. If they take 25 seconds to cross each other then their speed is?
A

10 km/hr

B

36 km/hr

C

48 km/hr

D

19 km/hr

Question 26 Explanation:
Given that, the speed and length of two trains are equal
And, they are moving in the opposite direction, they take 25 seconds to cross each other
Let the required speed of the trains be X m/sec
Now, from the formula (a + b)/(u + v), we have a = b = 250 m and u = v = X m/sec
Then, a + b = 250 + 250 = 500 m and u + v = 2X m/sec,
25 = 500/2X sec
X = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr
Hence, the speed of two trains is 36 km/hr
And, they are moving in the opposite direction, they take 25 seconds to cross each other
Let the required speed of the trains be X m/sec
Now, from the formula (a + b)/(u + v), we have a = b = 250 m and u = v = X m/sec
Then, a + b = 250 + 250 = 500 m and u + v = 2X m/sec,
25 = 500/2X sec
X = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr
Hence, the speed of two trains is 36 km/hr
Question 27

There is a 200 miles long tunnel. One train enters the tunnel at a speed of 200mph at the same time another train enters the tunnel in opposite direction at a speed of 1000 mph. A bee travels at a speed of 1500mph enters the tunnel goes to and fro until it reaches a train. What is the distance covered by the bee when the two trains collide?
A

280 miles

B

350 miles

C

250 miles

D

140 miles

Question 27 Explanation:
Relative speed of two trains = 1000+200 = 1200mph
Time taken to collide = 200/1200 = 1/6 hours
The bee travels for 1/6 hours. Hence distance covered = 1500 * 1/6 = 250 miles
Time taken to collide = 200/1200 = 1/6 hours
The bee travels for 1/6 hours. Hence distance covered = 1500 * 1/6 = 250 miles
Question 28

A train crosses a platform of 120m in 15sec, same train crosses another platform of length 180m in 18sec. then find the length of the train?
A

175m

B

180m

C

185m

D

170m

Question 28 Explanation:
Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Question 29

A 1200m long train crosses a tree in 120sec, how much time will I take to pass a platform 700m long?
A

180 sec

B

190 sec

C

170 sec

D

175 sec

Question 29 Explanation:
L = S*T
S= 1200/120
S= 10M/Sec
Total length(D)= 1900m
T = D/S
T = 1900/10
T = 190Sec
S= 1200/120
S= 10M/Sec
Total length(D)= 1900m
T = D/S
T = 1900/10
T = 190Sec
Question 30

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A

150 m

B

160 m

C

240 m

D

245 m

Question 30 Explanation:
Speed = 45 x 5/18 m/sec = 25/2 m/sec
Time = 30 sec
Let the length of bridge be x metres
Then, (130 + x)/30 = 25/2
2(130 + x) = 750
x = 245 m
Time = 30 sec
Let the length of bridge be x metres
Then, (130 + x)/30 = 25/2
2(130 + x) = 750
x = 245 m
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