# Trains

Problems on Trains: Problems on Trains Formulas and Shortcuts, Train Problems in Aptitude Questions with Solutions

## Problems on Trains: Problems on Trains Formulas and Shortcuts, Train Problems in Aptitude Questions with Solutions

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1 Tips

## Learning Pundits Content Team

__2 TIPS on cracking Aptitude Questions on Trains__

__2 TIPS on cracking Aptitude Questions on Trains__Looking for Questions instead of tips?- You can directly jump to Aptitude Test Questions using Trains

__Tip #1__: Understand the concepts involved in a train crossing a pole or a platform

1. Time taken by a train of length L to pass a pole or standing man or a signal post is equal to the time taken by the train to cover distance L.

2. Time taken by a train of length L to pass a station of length b is the time taken by the train to cover the distance (L + b).

**Question: **A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

**Solution: **

Time taken to cross a pole = time taken to cover distance equal to its own length.

Speed of the train in m/s = 60 x 5 / 18 = (50/3) m/s.

Length of the train = Speed of the train x Time taken to cross the pole

= 50/3 x 9

= **Length of the train = 150m.**

**Question:** A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr, what is the length of the platform?

**Solution: **

Speed of the train in m/s = 54 x 5 / 18 = 15m/s.

Length of the train = 15 x 20 = 300m.

Distance traveled in 36s = 15 x 36 = 540m. **(This is the length of the train + platform combined)**

**Length of the platform = (540 – 200) m = 240m.**

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__Tip #2__: For problems on 2 trains, use the concept of relative velocity

1. If two trains of length a and b are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = (a + b) / (u + v).

2. If two trains of length a and b are moving in the same direction at u m/s and v m/s, then time taken by the faster train to cross the slower train = (a + b) / (u - v) .

**Question: **2 trains of length 137 m and 163 m are running towards each other and speeds 42 km/hr and 48 km/hr respectively. In what time will the two trains cross each other?

**Solution: **

Relative velocity = 42 + 48 = 90 km/hr = (90 x 5/18) m/s = 25 m/s. *(Opposite directions)*

**Time taken to cross each other = 300 / 25 = 12 sec.**

**Question: **2 trains running in opposite directions cross a man standing on the platform in 27s and 17s respectively and they cross each other in 23s. Find the ratio of their speeds.

**Solution: **

Let the speeds be x m/s and y m/s respectively.

Then, length of 1^{st} train = 27x and that of 2^{nd} train = 17y.

Time taken to cross each other = (27x + 17y) / (x + y) = 23.

= 27x + 17y = 23x + 23y.

= 4x = 6y.

= ** x: y = 3 : 2.**

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# Trains

Problems on Trains: Problems on Trains Formulas and Shortcuts, Train Problems in Aptitude Questions with Solutions

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