Problems on Trains

1.

A train 110 m long is running with speed of 60 km/hr .In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?

   A.) 6 sec
   B.) 7 sec
   C.) 10 sec
   D.) 5 sec

Answer: Option 'A'

Relative speed = Train speed + Man Speed = 60 + 6 = 66 kmph = 18 1/3 m /sec
Distance to be covered = 110 meter
Time taken = Speed / Distance = 110 / (18 1/3) = (110 / 55) x 3 = 2 x 3 = 6 sec

2.

A train 240 m long passed a pole in 24 seconds .How long will it take to pass a platform 650 m long?

   A.) 150 sec
   B.) 100 sec
   C.) 65 sec
   D.) 89 sec

Answer: Option 'D'

89 sec

3.

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?

   A.) 25
   B.) 30
   C.) 40
   D.) 45

Answer: Option 'B'

Given, Length of the train = 500 m
Speed of the man = 3 km/hr
Speed of the train = 63 km/hr
Time taken by the train to cross a man = Length of the train / (speed of the train – speed of the man)
=> Time = 500 m / (63 – 3) km/hr
=> Time = 500 m / 60 km/hr
(to convert 60 km/hr to m/sec)
=> Time = 500 m / [60 × (5/18) m/sec]
=> Time = {500 / [60 × (5/18)]} sec
=> Time = {(500 × 18) / (60 × 5)} sec
=>Time = 30 sec

4.

Two trains 145 m and 155 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time taken by them to completely cross each other in seconds is

   A.) 10.8
   B.) 9.5
   C.) 10.75
   D.) 11

Answer: Option 'A'

Given, Length of 1st train = 145 m
Length of 2nd train = 155 m
Total length of two trains = 145 + 155 = 300 m
Speed of1st train = 60 kmph
Speed of 2nd train = 40 kmph
Since the two trains are moving in opposite direction, speed can be added.
=> Relative speed = Speed of1st train +Speed of 2nd train
60 + 40 = 100 kmph
--> Converting into m/sec
= 100 x (5/18) m/sec
= 250 / 9 m/sec
=>Relative speed =250 / 9 m/sec
Time taken by the trains to completely cross each other
 = Total length of two trains /Relative speed
= 300/ (250 /9)
= (300 × 9) / 250
=2700 / 250
= 10.8 sec
Thus,Time taken by the trains to completely cross each other = 10.8 sec

5.

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

   A.) 48 seconds
   B.) 42 seconds
   C.) 40 seconds
   D.) 45 seconds

Answer: Option 'C'

Given, Length of train =360 m
Length of bridge =140 m
Speed of train = 45 km/hr ---> Converting into meter/ second
= 45 × (5/18) m / sec
= 12.5 m/sec
=>Speed of train =12.5 m/sec
Required Time =(Length of train + Length of bridge) /Speed of train
= (360 + 140) / 12.5
= 500 / 12.5
= 40 sec
=>Required Time =40 sec

6.

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.) 79.2 km/hr
   D.) 79 km/hr

Answer: Option 'C'

Let the length of the train be x metres and its speed by y m/sec.
Time = Length / Speed of the train
Given,A train moves past a telegraph post in 8 seconds.
Then, x/y = 8
=> x = 8y
Now, the same train moves past a bridge of 264 m long in 20 seconds.
=> (x + 264) / y = 20
Subs x = 8y in the above eqn, we get
=> (8y + 264) = 20y
=> 20y - 8y = 264
=> 12y = 264
=> y = 22.
Therefore Speed = 22 m/sec = ( 22 x 18 /5) km/hr = 79.2 km/hr.

7.

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.) 55 m
   C.) 50 m
   D.) 65 m

Answer: Option 'C'

2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.
4 kmph = (4 x 5/18 m/sec = 10/9 m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then, ( x/(y - 5) = 9 and ( x/(y - 10) = 10.
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.

8.

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: 

   A.) 2 : 3
   B.) 6 : 7
   C.) 4 : 3
   D.) 9 : 16

Answer: Option 'C'

Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

9.

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'

2 kmph = ( 2x 5/18 ) m/sec = 5/9 m/sec 4 kmph = ( 4x 5/18 ) m/sec = 10/9 m/sec
Let the length of the train be x metres and its speed by y m/sec.
Then, ( x / y - 5/9 ) = 9 and ( x / y - 10 /9 ) = 10 .
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.

10.

The two trains of lengths 400m, 600m respectively, running at same directions. The faster train can Cross the slower train in 180sec, the speed of the slower train is 48km. then find the speed of the Faster train? 

   A.) 58 Kmph
   B.) 68 Kmph
   C.) 78 kmph
   D.) 55 Kmph

Answer: Option 'B'

Length of the two trains = 600m + 400m 
Speed of the first train = X 
Speed of the second train= 48 Kmph 
1000/X - 48 = 180 
1000/x - 48 * 5/18 = 180 
50 = 9X - 120 
X = 68 Kmph 

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