Aptitude-Problems on Trains.pdf

Quantitative Aptitude: Problems on Trains
Dr. Manjunatha. P
manjup.jnnce@gmail.com
Professor & Dean Academics
JNNCE Shimoga
Dept. of ECE
J.N.N. College of Engineering, Shimoga

Problems on Trains
Formula to convert Km/hr to m/s
1 hour = 60 × 60 = 3600 seconds
1 km = 1000 meters
x km/hr = x
1000
3600
= x
10
36
= x
5
18
m/s
Dr. Manjunatha. P (JNNCE) Quantitative Aptitude: Problems on Trains October 19, 2022 2 / 18

Problems on Trains
Formula to convert Km/hr to m/s
1 hour = 60 × 60 = 3600 seconds
1 km = 1000 meters
x km/hr = x
1000
3600
= x
10
36
= x
5
18
m/s
Formula to convert m/s to Km/hr
1 second =
1
60 × 60
=
1
3600
hour
1 meter =
1
1000
km
x m/s = x
1/1000
1/3600
= x
3600
1000
= x
36
10
= x
18
5
km/hr

Problems on Trains
Important Points to be considered for solving problems on moving trains:

Problems on Trains
1 The distance traveled by a train to cross a pole or person is equal to the
length of the train.

Problems on Trains
2 The distance traveled by train when it crosses a platform is equal to the
sum of the length of the train and length of the platform.

Problems on Trains
3 When two trains are traveling in opposite directions at speeds v1 m/s and
v2 m/s then their relative speed is the sum of their individual speeds
(v1 + v2) m/s.

Problems on Trains
3 When two trains are traveling in opposite directions at speeds v1 m/s and
v2 m/s then their relative speed is the sum of their individual speeds
(v1 + v2) m/s.
4 Two trains are traveling in the same direction at v1 m/s and v2 m/s
where v1 > v2 then their relative speed will be equal to the difference
between their individual speeds (v1 − v2) m/s.

Problems on Trains
5 When two trains of length x meters and y meters are moving in opposite
direction at v1 m/s and v2 m/s then the time taken by the trains to
cross each other is x+y
v1+v2

Problems on Trains
5 When two trains of length x meters and y meters are moving in opposite
direction at v1 m/s and v2 m/s then the time taken by the trains to
cross each other is x+y
v1+v2
6 When two trains of length x meters and y meters are moving in same
direction at v1 and v2 where v1 > v2 then the time taken by the faster
train to cross the slower train = x+y
v1−v2

Problems on Trains Problems on Pole/Man standing in the platform
Q1 A train running at the speed of 60 km/hr. It crosses a certain
pole that is in the way in 9 seconds. What is the length of the train?

Solution:

Solution:
60km/hr = 60 ×
5
18
=
50
3
m/s

Solution:
60km/hr = 60 ×
5
18
=
50
3
m/s
The length of both the train is

Solution:
60km/hr = 60 ×
5
18
=
50
3
m/s
Distance = Speed × Time
=
50
3
× 9
= 150 m

Q2 A train running at the speed of 56 km/hr crosses a pole in 18
seconds. What is the length of the train?

Solution:

Solution:
56km/hr = 56 ×
5
18
=
140
9
m/s

Solution:
56km/hr = 56 ×
5
18
=
140
9
m/s
=
140
9
× 18
= 280 m

Q3 A train moving at speed of 90 km/hr crosses a pole in 7 seconds.
Find the length of the train.

Solution:

Solution:
90km/hr = 90 ×
5
18
= 25 m/s

Solution:
90km/hr = 90 ×
5
18
= 25 m/s
= 25 × 7
= 175 m

Problems on Trains Platform/Bridge/Tunnel
Q1 A 90 m long train is running at a speed of 54 km/hr. If it takes
30 seconds to cross a platform, find the length of the platform.

Solution:

Solution:
54 kmph = 54 × 5
18 = 15 m/s

Solution:
54 kmph = 54 × 5
18 = 15 m/s
Time to cross the bridge = 30 sec

Solution:
54 kmph = 54 × 5
18 = 15 m/s
Distance to cross the platform

Solution:
54 kmph = 54 × 5
18 = 15 m/s
= 15 × 30 = 450 m

Solution:
54 kmph = 54 × 5
18 = 15 m/s
= 15 × 30 = 450 m
Distance to cross the platform =length of train + length of platform

Solution:
54 kmph = 54 × 5
18 = 15 m/s
= 15 × 30 = 450 m
Distance to cross the platform =length of train + length of platform
Length of platform=450-90=360 m

Q2 A train 175 m long crosses a bridge which is 125 m long in 80
seconds. What is the speed of the train?

Solution:

Solution:
Length of Train = 175 m

Solution:
Length of Train = 175 m Length of bridge = 125 m

Solution:
Distance to cross the bridge =length of train + length of bridge

Solution:
Distance to cross the bridge =175+125=400 m

Solution:
Speed of the train is

Solution:
Speed of the train is
Speed =
Distance
Time
=
400
80
= 5 m/sec

Q3 A train 220 m long is running at a speed of 36 km/hr. What time
will it take to cross a 110 m long tunnel?

Solution:
Length of Train = 220 m, Length of tunnel = 110 m

Solution:
Total length=220+110=330 m

Solution:
Total length=220+110=330 m Speed of train 36 km/hr
36kmph = 36 × 5
18 = 10 m/s

Solution:
36kmph = 36 × 5
18 = 10 m/s
The time taken by a train to cross the tunnel is:

Solution:
36kmph = 36 × 5
18 = 10 m/s
Time =
Distance
Speed
=
330
10
= 33 seconds

Q4 Find the time taken by 150 m long train passes through a bridge
which is 100 m long, running at a speed of 72 km/hr.

Solution:

Solution:
Length of Train = 150 m, Length of bridge = 100 m

Solution:
Total length=150+100=250 m

Solution:

Solution:
72kmph = 72 × 5
18 = 20 m/s

Solution:
72kmph = 72 × 5
18 = 20 m/s
Time =
Distance
Speed
=
250
20
= 12.5 seconds

Problems on Trains Moving in the Opposite direction
Q1 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

Solution:

Solution:
x is the speed of first train

Solution:
y is the speed of second train

Solution:
Speed of one train is twice the speed of the other train

Solution:
y = 2x
Total length of both the trains is 100+100 = 200 m

Solution:
y = 2x
Distance = Speed × T ime

Solution:
y = 2x
In this case the length of both the trains is equal to
the distance traveled.

Solution:
y = 2x
T ime =
Distance
Speed
8 =
200
x + y
=
200
x + 2x
3x =
200
8
= 25
x =
25
3
m/sec
=
25
3
×
18
5
km/sec
= 30 km/hr

Solution:
y = 2x
T ime =
Distance
Speed
8 =
200
x + y
=
200
x + 2x
3x =
200
8
= 25
x =
25
3
m/sec
=
25
3
×
18
5
km/sec
= 30 km/hr
y = 2x = 2 × 30 km/hr
= 60 km/hr

Solution:

Solution:
y = 2x

Solution:
y = 2x
T ime =
Distance
Speed
12 =
200
x + y
=
200
x + 2x
3x =
200
12
=
50
3
m/sec
x =
50
9
m/sec
=
50
9
×
18
5
km/sec
= 20 km/hr

Solution:
y = 2x
T ime =
Distance
Speed
12 =
200
x + y
=
200
x + 2x
3x =
200
12
=
50
3
m/sec
x =
50
9
m/sec
=
50
9
×
18
5
km/sec
= 20 km/hr
y = 2x = 2 × 20 km/hr
= 40 km/hr

Solution:

Solution:
y = 2x

Solution:
y = 2x
T ime =
Distance
Speed
20 =
200
x + y
=
200
x + 2x
3x =
200
20
= 10 m/sec
x =
10
3
m/sec
=
10
3
×
18
5
km/sec
= 12 km/hr

Solution:
y = 2x
T ime =
Distance
Speed
20 =
200
x + y
=
200
x + 2x
3x =
200
20
= 10 m/sec
x =
10
3
m/sec
=
10
3
×
18
5
km/sec
= 12 km/hr
y = 2x = 2 × 12 km/hr
= 24 km/hr

Q4 Two trains of length 150 m and 170 m respectively are running at
the speed of 40 km/hr and 32 km/hr on parallel tracks in opposite
directions. In what time will they cross each other?

Solution:
Relative speed of train = (40+32) km/hr

Solution:
72km/hr = 72 ×
5
18
m/sec
= 20m/sec

Solution:
72km/hr = 72 ×
5
18
m/sec
= 20m/sec
Total length of both the trains is
150 + 170 = 320 m

Solution:
72km/hr = 72 ×
5
18
m/sec
= 20m/sec
150 + 170 = 320 m
Time to cross each other is
Time =
Distance
Speed
=
320
20
= 16 sec

Problems on Trains Moving in the Same Direction
Q1 A train of 900 m long moves at 90 kmph can cross another train
of 1200 m long moving in the same direction in 3 min. What is the
speed of the second train?

Solution:

Solution:
time t = 3 min or

Solution:
time t = 3 min or
time t = 3
60 = 1
20hr

Solution:
time t = 3 min or
time t = 3
60 = 1
20hr
1200 + 900 = 2100 = 2.1km

Solution:
time t = 3 min or
time t = 3
60 = 1
20hr
1200 + 900 = 2100 = 2.1km
Speed =
Distance
Time
90 − x =
2.1
1/20
= 42
x = 90 − 42 = 48 km/hr

Q2 Two trains 130 m and 140 m long are running on parallel tracks in
the same direction with a speed of 68 km/hr and 50 km/hr. How
long will it take to clear off each other from the moment they meet?

Solution:

Solution:
Relative speed of trains

Solution:
= 68 − 50 = 18 km/hr
= 18 ×
5
18
= 5 m/sec

Solution:
= 68 − 50 = 18 km/hr
= 18 ×
5
18
= 5 m/sec
Total length of both the trains

Solution:
= 68 − 50 = 18 km/hr
= 18 ×
5
18
= 5 m/sec
130+140=270 m

Solution:
= 68 − 50 = 18 km/hr
= 18 ×
5
18
= 5 m/sec
130+140=270 m
Time to clear off each other

Solution:
= 68 − 50 = 18 km/hr
= 18 ×
5
18
= 5 m/sec
130+140=270 m
Time to clear off each other
Time =
Distance
Speed
=
270
5
= 54 sec

Q3 The two trains are running on parallel tracks in the same direction
at 70 km/hr and 50 km/hr respectively. The faster train passes a
man 27 second faster than the slower train. Find the length of the
faster train.

faster train.
Solution:

faster train.
Solution:
= 70 − 50 = 20 km/hr
= 20 ×
5
18
=
50
9
m/sec

faster train.
Solution:
= 70 − 50 = 20 km/hr
= 20 ×
5
18
=
50
9
m/sec
Length of the faster train
Distance = Time × Speed
=
50
9
× 27 = 150 m

Aptitude-Problems on Trains.pdf

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