Tackling ‘train’ questions in ‘time and distance’ for Police recruitment exam

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Distance topic. Trains: It is a part of Time and Distance. The train-based questions depend on time, distance and speed. Before the question, first, let […]

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Distance topic.

Trains: It is a part of Time and Distance. The train-based questions depend on time, distance and speed. Before the question, first, let us will discuss the basics in trains.

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* If a train has to cover a standing person or a tree or pole, then train has to cover its own length.
Here Distance = Length of the train

* If a train has to cross a platform or a bridge, then train has to cover the sum of lengths of train and platform or bridge.
Here Distance = Sum of lengths of train and platform or bridge

* If two trains are running in the same direction, when they cross each and other, the distance and relative speeds are as follow:
Distance = Sum of lengths of two trains
Relative Speed = Difference between speeds of two trains
So, the time taken by the trains to cross each other = Distance/Speed

* However, if two trains are running in opposite direction, when they cross each and other, the distance and relative speeds are as follow.
Distance = Sum of lengths of two trains
Relative Speed = Sum of speeds of two trains
So, the time taken by the trains to cross each other = Distance/Speed

Now, we will discuss some examples:

1. 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. Then, find the ratio of their speeds.
Solution:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres
And the length of the second train = 17y metres.
(27x 17y)/(x y) =23
27x 17y = 23x 23y
4x = 6y
x/y = 3:2

2. The 200 m and 250 m lengths of two trains are running at 45 km/hr and 99 km/hr respectively. If they are running in the same direction on parallel railway tracks, then at what time will they cross each other.
Solution:
Distance = 200 250 = 450 m
Relative Speed = 99 – 45 = 54 km/hr = 54 ×5/18 = 15 m/s
Time = 450 / 15 = 30 Seconds

3. A train crosses a standing person in 12 seconds and it will cross 120 m length of platform in 16 seconds. Find the length and speed of train?
Solution:
Let length of train = x m
Distance = x m, Time = 12 seconds
The train will cover ‘x’ plus extra 120 m in 16 seconds.
Therefore, the train will cover 120 m in 16 – 12 = 4 seconds
Distance = 120 m
Time = 4 seconds
Speed = 120/4 = 30 m/s
Length of the train = 12 × 30 = 360 m

4. 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, then what is the length of the platform?
Solution:
Speed = 54 km/hr = 54 ×5/18 = 15 m/s
Length of the train = 20 × 15 = 300 m
Let the length of the platform is ‘x’ m
Then (x 300)/36=15
x 300 = 540
x = 540 – 300 = 240 m
Therefore, the length of the platform = 240 m

5. Say, 300 m and 400 m lengths of two trains are running at 88 km/hr and 92 km/hr respectively. If they are running in opposite direction on parallel railway tracks, then at what time they cross each and other?
Solution:
Distance = 300 400 = 700 m
Relative Speed = 88 92 = 180 km/hr = 180 × 5/18 = 50 m/s
Time = 700 / 50 = 14 sec.

6. About 240 m length of train is running at 80 km/hr. Then, at what time it will cross a girl, who is running at 8 km/hr in the same direction?
Solution:
Distance = 240 m
Relative Speed = 80 – 8 = 72 km/hr = 20 m/s
Time = 240 / 20 = 12 sec

7. Say, 350 m length of train is running at 82 km/hr. Then, at what time it will cross a boy, who is running at 8 km/hr in the opposite direction?
Solution:
Distance = 350 m
Relative Speed = 82 8 = 90 km/hr = 25 m/s
Time = 350/ 25 = 14 sec

Banda Ravipal Reddy
Director, SIGMA
Sai Institute of General Mental Ability
Hyderabad
Ph. 9491614131

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