Problems on Trains Aptitude Solved Examples - Set 02

Problems on Trains Questions and Answers with Detailed Solution:


Question No. 01
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
Answer: Option A
Explanation:
Let the length of each train be x meters.
Then, distance covered = 2x meters.
Relative speed = (46 - 36) km/hr
                           = [10 × (5/18)] m/sec
                           = (25/9) m/sec
2x/36 = 25/9
=> 2x = 100
=> x = 50.

Question No. 02
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.
Answer: Option B
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.

Question No. 03
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
(A) 45 m
(B) 50 m
(C) 54 m
(D) 72 m
Answer: Option B
Explanation:
2 kmph = [2 × (5/18)] m/sec = (5/9) m/sec
4 kmph = [4 × (5/18)] m/sec = (10/9) m/sec
Let the length of the train be x meters and its speed by y m/sec.
Then, [x/{y - (5/9)}] = 9 and [x/{y - (10/9)}] = 10
 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100
On solving, we get: x = 50
 Length of the train is 50 m.

Question No. 04
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?
(A) 69.5 km/hr
(B) 70 km/hr
(C) 79 km/hr
(D) 79.2 km/hr
Answer: Option D
Explanation:
Let the length of the train be x meters and its speed by y m/sec.
Then, x/y = 8
=> x = 8y
Now, [(x + 264)/20] = y
=> 8y + 264 = 20y
=> y = 22
 Speed = 22 m/sec = [22 × (18/5)] km/hr = 79.2 km/hr.

Question No. 05
A train traveling at 48 kmph completely crosses another train having half its length and traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is:
(A) 400 m
(B) 450 m
(C) 560 m
(D) 600 m
Answer: Option A
Explanation:
Let the length of the first train be x meters.
Then, the length of the second train is (x/2) meters
Relative speed = (48 + 42) kmph = [90 × (5/18)] m/sec = 25 m/sec
[x + (x/2)]/25 = 12
Or, (3x/2) = 300
Or, x = 200
 Length of first train = 200 m.
Let the length of platform be y meters.
Speed of the first train = [48 × (5/18)] m/sec = (40/3) m/sec
 [(200 + y) × (3/40)] = 45
=> 600 + 3y = 1800
=> y = 400 m.

Question No. 06
Two goods train 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.
(A) 12 sec
(B) 24 sec
(C) 48 sec
(D) 60 sec
Answer: Option B
Explanation:
Relative speed = (45 + 30) km/hr = [75 × (5/18)] m/sec = (125/6) 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 × (6/125)] = 24 sec.

Question No. 07
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
Answer: Option C
Explanation:
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
(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.

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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