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Problems on Trains - Aptitude Questions and Answers - RejinpaulPlacement




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57.
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Answer & Solution
Answer: (B) 4 : 3

Solution:

Let us name the trains as A and B. Then,

(A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3.

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58.
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?
Answer & Solution
Answer: (B) 10 a.m.

Solution:

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.

Therefore 20x + 25(x - 1) = 110

=> 45x = 135

=> x = 3.

So, they meet at 10 a.m.

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59.
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 & Solution
Answer: (A) 400 m

Solution:

Let the length of the first train be x metres.

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

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

Therefore [x + (x/2)] = 12 or 3x = 300     or     x = 200.
25 2

Therefore Length of first train = 200 m.

Let the length of platform be y metres.

Speed of the first train = ( 48 x 5 ( m/sec = 40 m/sec.
18 3

Therefore (200 + y) x 3 = 45
40

=> 600 + 3y = 1800

=> y = 400 m.

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60.
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 & Solution
Answer: (D) 81 km/hr

Solution:

4.5 km/hr = ( 4.5 x 5 ( m/sec = 5 m/sec = 1.25 m/sec, and
18 4

5.4 km/hr = ( 5.4 x 5 ( m/sec = 3 m/sec = 1.5 m/sec.
18 2

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

Therefore Speed of the train = ( 22.5 x 18 ( km/hr = 81 km/hr.
5

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61.
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 & Solution
Answer: (B) 50 m

Solution:

2 kmph = ( 2 x 5 ( m/sec = 5 m/sec.
18 9

4 kmph = ( 4 x 5 ( m/sec = 10 m/sec.
18 9

Let the length of the train be x metres and its speed by y m/sec.

Then, ( x ( = 9 and ( x ( = 10.
y - 5
9
y - 10
9

Therefore 9y - 5 = x and 10(9y - 10) = 9x

=> 9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

Therefore Length of the train is 50 m.

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62.
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Answer & Solution
Answer: (C) 27 7/9 m

Solution:

Relative speed = (40 - 20) km/hr = ( 20 x 5 ( m/sec = ( 50 ( m/sec.
18 9

Therefore Length of faster train = ( 50 x 5 ( m = 250 m = 27 7 m.
9 9 9

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63.
How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Answer & Solution
Answer: (B) 30

Solution:

Speed of the train relative to man = (63 - 3) km/hr
= 60 km/hr
= ( 60 x 5 ( m/sec
18
= ( 50 ( m/sec.
3
Therefore Time taken to pass the man
= ( 500 x 3 ( sec
50
= 30 sec.

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