## [Aptitude] Trains, Platforms TSD (Time,Speed,Distance) made easy

**Main-Topic:** Time, Speed Distance (TSD)

**Subtopic:** Trains and Platforms.

you’ll be given some data and asked to find the length of railway platform or speed of train etc.

- Visualizing the Concept: Train and Pen
- Case 1: One Train One Man (or Tree, Pole)
- Case 2: One Train One Platform (or bridge, tunnel)
- Case 3: Two Trains
- Unit Conversions
- Previous Articles on Aptitude

# Visulize: Pen and Train

Before going into Trains concept, try to visulize following. (ofcourse technically incorrect but for concept clarity)

You must have seen the advertizement of a ballpen “Flair Writometer”. They claim it can write for 2,500 metres and even provide a marking scale on the ballpen refill to measure the ‘distance’! See the photo

So You’re standing on a Railway platform, holding that writometer pen in your hand, pointing it straight towards the upcoming train’s side, like this photo

The train passes, and your pen makes a straight line on the entire body of this train.

Now you open the pen’s refill and check the markings, obviously few mili-litres of ink is used and marking would show that you’ve drawn a line of 200 meters.

Meaning length of this train is 200 m.

At the same time, your friend was sitting in the window seat of the same railway and he too held a writometer pen in his hand pointing it out of the window and towards the platform.So as the train passed, his pen also drew a straight line on the entire platform. Later he checks the refill of his pen: it drew a line of 1000 meters.

Meaning length of this railway platform is 1000 m.

so what is the total distance or length of lines drawn by the two pens?

200m of train + 1000m of platform = 1200m.

Now questions

# Case1: one men, one train.

A railway train running at the speed of 20 meter per second, crosses a man in 10 seconds. What is the length of the train?

For all the problems about train, boats, cars, scooters, men required to complete a job, tata nano and kingfisher airplane, in short TSDW (time,speed, distance, work) you need to remember only one “STD” formula

ST=D

speed (s) x time (t) = distance (d)

Back to the question, what is given?

Visualise the situation: you are the man, holding the writometer pen and the train crossed you in 10 seconds. What is the distance of the line drawn by your pen on the body of the train?

Speed (s)= 20 m/s (given)

Time (t)= 10 seconds (given)

so

s x t = d

20 x 10=200 m.

final answer: length of the train is 200 m.

## Alternatives:

Instead of man, they can rephrase and ask: Train crossed a “Tree, Telephone-pole, Tiger, Kalmadi, Raja..” The concept remains the same. Everybody is holding a pen.

# Case2: one platform, one train.

Question: a train running at the speed of 20 m/s, crosses a railway platform in 20 seconds. If the length of the train is 100 m, what is the length of this railway platform?

So in this case, you were standing on a platform holding a **blue** pen and I am sitting in the railway also holding a **purple** pen.

What is the total length of lines drawn by both of us?

Total Length (or distance)= Your **blue** pen drew 100 m line + My **purple** pen drew (x) m line.

: The total of **blue** and purple color line in above photo

So total distance covered by the train is (100+x)

Now ,

speed is given: 20m/s

time is also given: 20 seconds