Trains Aptitude Solved Examples - Set 01

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)/(xy) = 23
=> 27x + 17y = 23x + 23y
=> 4x = 6y
=> x/y = 3/2

Trains Aptitude:
Formula:                Trains Aptitude Formulas
Solved Examples:  Solved Examples: Set 01     Solved Examples: Set 02
Practice Test:         Practice Test: 01     Practice Test: 02
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