Trains Aptitude Questions and Answers with Detailed Solution:
Question No. 01
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?
(A) 320 m
(B) 350 m
(C) 650 m
(D) None of
these
Answer:
Option B
Explanation:
Speed =
(300/18) m/sec = (50/3) m/sec.
Let the
length of the platform be x meters.
Then, [(x +
300)/39] = 50/3
=> 3(x + 300) = 1950
=> x = 350 m.
Question No. 02
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) 120 m
Answer:
Option B
Explanation:
Speed = [54
× (5/18)] m/sec = 15 m/sec
Length of
the train = (15 × 20) m = 300 m.
Let the
length of the platform be x meters.
Then, (x + 300)/36 = 15
=> x + 300 = 540
=> x = 240 m.
Question No. 03
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:
Option D
Explanation:
Speed = [72×
(5/18)] m/sec = 20 m/sec
Time = 26
sec.
Let the
length of the train be x meters.
Then, (x +
250)/26 = 20
=> x + 250 = 520
=> x = 270
Question No. 04
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:
(A) 130 m
(B) 360 m
(C) 500 m
(D) 540 m
Answer:
Option C
Explanation:
Speed = [78
× (5/18)] m/sec = (65/3) m/sec
Time = 1
minute = 60 seconds.
Let the
length of the tunnel be x meters.
Then, [(800
+ x)/60] = 65/3
=> 3(800 + x) = 3900
=> x = 500.
Question No. 05
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) None of
these
Answer:
Option B
Explanation:
Let the
length of the train be x meters and its speed by y m/sec.
Then, x/y
= 15
=> y = x/15
∴ [(x +
100)/25] = x/15
=> 15(x + 100) = 25x
=> 15x + 1500 = 25x
=> 1500 = 10x
=> x = 150 m.
Question No. 06
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:
Option D
Explanation:
4.5 km/hr =
[4.5 × (5/18)] m/sec = (5/4) m/sec = 1.25 m/sec, and
5.4 km/hr =
[5.4 × (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 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 = [2.25 × (18/5)] km/hr = 81 km/hr
Question No. 07
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?
(A) 230 m
(B) 240 m
(C) 250 m
(D) None of
these
Answer:
Option A
Explanation:
Relative
speed = (120 + 80) km/hr = [200 × (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
Question No. 08
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
Answer:
Option B
Explanation:
Speed of the
train relative to man = (125/10) m/sec
= (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 No. 09
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:
(A) 10
(B) 18
(C) 36
(D) 72
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 × (18/5)]
km/hr = 36 km/hr.
Question No. 10
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
Answer:
Option B
Explanation:
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 length
of the second train = 17y meters.
∴ (27x +
17y)/(x+ y) = 23
=> 27x + 17y =
23x + 23y
=> 4x = 6y
=> x/y = 3/2
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