# Problems on Trains - Aptitude Questions and Answers - RejinpaulPlacement

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50.
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:
Answer: (B) 50 m

Solution:   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 metres and its speed be 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.
51.
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?
Answer: (D) 81 km/hr

Solution:   4.5 km/hr = [4.5 * (5/18)] m/sec = (5/4) m/sec = 1.25 m/sec

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) * 84 = (x - 1.5) * 8.5
=> 8.4 x – 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5

Speed of the train = [22.5 (18/5)] km/hr = 81 km/hr.
52.
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: [C.D.S. 2001]
Answer: (C) 60 km/hr

Solution:   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
53.
A train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train is:
Answer: (D) 99 km/hr

Solution:   Speed of the first train = (150/15) m/sec = 10 m/sec.

Let the speed of second train be x m/sec.

Relative speed = (10 +x) m/sec.

300 / (10 + x) = 8
=> 300 = 80 + 8x
=> x = 220/8 = (55/2) m/sec

So, speed of the second train = [(55/2) * (18/5)] kmph = 99 kmph.
54.
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is:
Answer: (B) 400 m

Solution:   Let the length of the first train be x metres.

Then, the length of the second train is (x/2) metres.

Relative speed = (48 + 42) kmph = [90 * (5/18)] m/sec = 25 m/sec.

[x + (x/2)] / 25 = 12 => 3x / 2 = 300 => x = 200

Length of the first train = 200 m.

Let the length of platform be y metres.

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.
55.
Two trains running in opposite directions cross a man standing on the platform is 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: [Hotel Management 1997]
Answer: (B) 3 : 2

Solution:   Let the speed of the two trains be x m/sec and y m/sec respectively.

Then, speed of the first train = 27x metres

Length of the second train = 17y metres.

(27x + 17y) / (x + y) = 23
=> 27x + 17y = 23x + 23y
=> 4x = 6y
=> x/y = 3/2.
56.
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7a.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?