# 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 […]

Published Date - 11:02 PM, Sat - 7 May 22

**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.

* 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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