Aptitude session for CF students
Problems on Train
1) A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the
length of the train?
120 m
180 m
324 m
150 m
5 50
Speed 60
=
= x 18 3
m/sec
m/sec
.
Length of the train = (Speed x Time).
50
Length of the x
) m = 150
train = 9
3
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:
45 km/hr
50 km/hr
54 km/hr
55 km/hr
125
Speed of the train relative to man
=
10
m/sec
25
=
2
m/sec.
25 18
= x
2 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.
3) The length of the bridge, which a train 130 meters long and traveling at 45 km/hr can
cross in 30 seconds, is:
200 m
225 m
245 m
250 m
5 25
Speed 45
=
= x
18 2
m/sec m/sec.
Time = 30 sec.
Let the length of the bridge be x meters.
130 + x 25
Then, =
30 2
2(130 + x) = 750
x = 245 m.
4) 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:
1:3
3:2
3:4
None of these
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x meters,
and the length of the second train = 17y meters.
27x + 17y
= 23
x+ y
27x + 17y = 23x + 23y
4x = 6y
x 3
= .
y 2
=3:2
5) 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?
120 m
240 m
300 m
None of these
5
Speed 54
= x m/sec = 15
18 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x meters.
x + 300
Then, = 15
36
x + 300 = 540
x = 240 m.
6) A train 240 m long passes a pole in 24 seconds. How long will it take to pass a
platform 650 m long?
65 sec
89 sec
100 sec
150 sec
240
Speed
= m/sec = 10
m/sec.
24
240 + 650
Required time
= sec = 89
sec.
10
7) 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:
50 m
72 m
80 m
82 m
Let the length of each train be x meters.
Then, distance covered = 2x meters.
Relative speed = (46 - 36) km/hr
= 10*
m/sec
18
25
=
m/sec
9
2x 25
36 9
2x = 100
x = 50.
8) 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?
40 sec
42 sec
45 sec
48 sec
m/s
Formula for converting from km/hr to m/s: X km/hr = Xx
.
18
5 25
Therefore, Speed 45 m/sec
=
= x .
m/sec
18 2
Total distance to be covered = (360 + 140) m = 500 m.
Distanc
e
Formula for finding Time =
Speed
500 x
2
Required time = 40
= sec.
sec
25
9) 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:
36, 45, 48, 49
Relative speed = (60+ 90) km/hr
150
=
x
m/sec
18
125
=
m/sec.
3
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time 2000
= x sec = 48
sec.
125
10) A jogger running at 9 kmph alongside a railway track 240 meters ahead of the
engine of a 120 meters long train running at 45 kmph in the same direction. In how
much time will the train pass the jogger?
3.6 sec
18 sec
36 sec
72 sec
Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.
36
=
x
m/sec
18
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
360
Time taken = 36
= sec.
sec
10
11) A 270 meters 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?
230 m
240 m
260 m
320 m
None of these
Relative speed = (120 + 80) km/hr
200
=
x
m/sec
18
500
=
m/sec.
9
Let the length of the other train be x meters.
x + 270 500
Then, =
9 9
x + 270 = 500
x = 230.
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?
230 m
240 m
260 m
270 m
Speed 72 = 20
= x m/sec.
m/sec
18
Time = 26 sec.
Let the length of the train be x meters.
x + 250
Then, = 20
26
x + 250 = 520
x = 270.
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:
30 km/hr
45 km/hr
60 km/hr
75 km/hr
Let the speed of the slower train be x m/sec.
Then, the speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
100 + 100
= 3x
24x = 200
25
x= .
50
So, speed of the faster train
m/sec
=
50 18
= x
km/hr
3 5
= 60 km/hr.
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:
9.6
10
10.8
5 250
100
Relative speed = (60 + 40) km/hr = =
x
m/sec m/sec.
18 9
Distance covered in crossing each other = (140 + 160) m = 300 m.
9 54
Required time 300 sec = 10.8
=
= x sec.
sec
250 5
15) A train 110 meters long is running at a speed of 60 kmph. In what time will a man
who is running at 6 kmph pass in the direction opposite to that in which the train is
going?
5 sec
6 sec
7 sec
10 sec
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
66
=
x
m/sec
18
55
=
m/sec.
3
3
Time taken to pass the man
110 x
= sec = 6
sec.
55
16) A train traveling 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?
2.5 min
3 min
3.2 min
3.5 min
Total distance
covered
7 1
mile
= +
s
2 4
15
= miles.
Time
taken
15
hr
=
s
4 x 75
hr
=
s
20
1
x min
=
60 .
20
= 3 min.
17) A train 800 meters 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:
130
360
500
540
5 65
Speed 78 m/sec
m/sec =
= x .
18 3
Time = 1 minute = 60 seconds.
Let the length of the tunnel be x meters.
800 + x 65
Then, =
60 3
3(800 + x) = 3900
x = 500.
18) A 300 meter long train crosses a platform in 39 seconds while it crosses a signal
pole in 18 seconds. What is the length of the platform?
320 m
350 m
650 m
Data inadequate
300 50
Speed m/sec m/sec
= = .
18 3
Let the length of the platform be x meters.
x + 300 50
Then, =
39 3
3(x + 300) = 1950
x = 350 m.
19) A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds.
Its length is:
50 m
150 m
200 m
Data inadequate
Let the length of the train be x meters and its speed by y m/sec.
x x
Then, = 15 y= .
y 15
x + 100 x
25 15
15(x + 100) = 25x
15x + 1500 = 25x
1500 = 10x
x = 150 m.
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?
69.5 km/hr
70 km/hr
79 km/hr
79.2 km/hr
Let the length of the train be x meters and its speed by y m/sec.
x
Then, =8 x = 8y
x + 264
Now, =y
20
8y + 264 = 20y
y = 22.
18
Speed = 22 m/sec 22 km/hr = 79.2
= x km/hr.
21) How many seconds will a 500 meter 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?
25
30
40
45
Speed of the train relative to man = (63 - 3) km/hr
= 60 km/hr
60
= m/sec
x
18
50
= m/sec
3
Time taken to pass the man
500
= sec
x
50
= 30 sec.
22) Two goods trains, 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.
12 sec
24 sec
48 sec
60 sec
Relative speed = = (45 + 30) km/hr
75
= m/sec
x
18
125
m/sec
=
.
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 = 24
= x sec.
125
23) Two trains are running in opposite directions with the same speed. If the length of
each train is 120 meters and they cross each other in 12 seconds, then the speed of
each train (in km/hr) is:
10
18
36
72
Let the speed of each train be x m/sec.
Then, the relative speed of the two trains = 2x m/sec. 2x = 20
=2X=120+120/12
2X=20
x = 10.
18
Speed of each train = 10 m/sec km/hr = 36
10x
= km/hr.
5
24) Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a
telegraph post. If the length of each train is 120 meters, in what time (in seconds) will
they cross each other traveling in opposite directions?
10
12
15
20
120
Speed of the first train m/sec = 12
= m/sec.
10
120
Speed of the second train m/sec = 8
= m/sec.
15
Relative speed = (12 + 8) = 20 m/sec.
120 + 120
Required time
sec = 12 sec.
=
20
25) A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long
coming from the opposite direction in 6 seconds. The speed of the second train is:
48 km/hr
54 km/hr
66 km/hr
82 km/hr
Here is the simplest form that you can understand.
Since the two trains travel in opp directions, add both speeds. the speed of one train is
given, let the speed of another train be x.
Speed=x+50 km/hr.
The relative distance = 108 + 112 = 220 m.
Time = 6 seconds.
Speed = distance/time.
x+50 = 220/6 m/s
x+50 = 110/3 *18/5(to convert m/s to km/hr ,since the answer required in km/hr)
x+50 = 132,
x = 82 km/hr.
