trains Topic-wise Practice Test, Examples With Solutions & More Shortcuts

trains & IT'S TYPES

Useful for Management (CAT, XAT, MAT, CMAT, IIFT, SNAP & other), Bank (PO & Clerk) SSC (CGL, 10+2, Steno, FCI, CPO, Multitasking), LIC (AAO & ADO) CLAT, RRB, UPSC and Other State PSC Exams

Model 1 Train Vs Train in same direction

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Model 2 Train Vs Train in opposite direction

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Model 3 Train Vs Bridge/Platform

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Model 4 Train Vs Pole/Signal Post/Man

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Model 5 Train Vs Both platform and a man/a pole

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Model 6 Change in speed Vs Change with time travel

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trains Topic-wise Types, Definitions, Important fact & Techniques with Short Tricks & Tips useful for all competitive Examinations

Trains - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

Useful For All Competitive Exams Like UPSC, SSC, BANK & RAILWAY

Posted By Careericons Team

Introduction to Trains:

In this topic you have to learn how much time the train will cross a person/ platform/ other, train or what will be the length of the train/ platform or relative speed of two trains or the speed of a train – kind of questions is asked. Some other types of questions like change in speeds, distance in the way or other special situations are also asked in various competitive exams.

Key Take-away Points:

Time taken in crossing 'b' metre length (i.e. platform, bridge, tunnel, standing train etc) by 'a' metre length train = total time taken in travelling (a + b) metre by the train.

Let a train is travelling at the speed x km/hr and in the same direction, another train is travelling on a parallel path with the speed y km/hr, then,

Relative speed of the faster train in same direction = (x – y) km/hr.

Suppose that a train is travelling with the speed 'x' km/hr and from the opposite direction another train is coming on a parallel path with the speed 'y' km/hr, then

Relative speed of the train in opposite direction = (x + y) km/hr


Top "6" Concepts To Solve Trains (Time, Speed & Distance) Based Aptitude Problems

In these questions topic, All the concepts are based on the moving trains are seen to cross an object (which is standing still like a Postbox or Tree or a Platform) or another moving object (another moving), the entire length of the train has to be considered. The object needs to be crossed entirely. This is the only thing you have to understand about the topic.

Trains-based problems are always given to find the length of the train travelled or going to travel, Time taken by the train to cross or the time needed to cross a bridge/ platform / another train in the same direction or opposite direction. To solve these types of problems, there are 6 basic concepts.

These 6 basic Concepts are based on Trains problems asked in various SSC, BANK, UPSC, Railway & other competitive exams. By learning these 6 methods/ concepts with formulas & examples you can solve all kinds of problems that you face in your upcoming examinations.

Let us see the Trains concepts one by one,

Concepts S.No Situations Basic Formula Expended Form of Basic Formula Expended Formula in Symbolic Form
Concept 1: When a train crosses a moving object with length in the opposite direction Relative Speed × Time = Distance (Speed of the train) + (Speed of theobject)
×
(Time taken by the train to cross the moving object)
=
(Length of the train) + (Length of the object)
$(S_T + S_0) × t =$
$(L_T + L_0)$
Concept 2: When a train crosses a moving object with length in the same direction Relative Speed × Time = Distance (Speed of the train) - (Speed of theobject)
×
(Time taken by the train to cross the moving object)
=
(Length of the train) + (Length of the object)
$(S_T - S_0) × t =$
$(L_T + L_0)$
Concept 3: When a train crosses a moving object without length like a man, a tree, a pole, a point etc. in opposite direction Relative Speed × Time = Distance (Speed of the train) + (Speed of theobject)
×
(Time taken by the train to cross the moving object)
=
(Length of the train)
$(S_T + S_0) × t =$
$L_T$
Concept 4: When a train crosses a moving object without length in the same direction Relative Speed × Time = Distance (Speed of the train) - (Speed of theobject)
×
(Time taken by the train to cross the moving object)
=
(Length of the train)
$(S_T - S_0) × t =$
$L_T$
Concept 5: When a train crosses a stationary object with length Relative Speed × Time = Distance (Speed of the train)
×
(Time taken to cross the stationary object)
=
(Length of the train) + (Length of the object)
$S_T × t =$
$L_T + L_0$
Concept 6: When a train crossing a stationary
object without length
Relative Speed × Time = Distance (Speed of the train)
×
(Time taken to cross the stationary object)
=
(Length of the train)
$S_T × t = L_T$

Where,

$S_T$ = Speed of the train, $S_0$ = Speed of the object, $L_T$ = Length of the train,

$L_0$ = Length of the object, t = time taken by the train to cross the object


"16" - Important Aptitude Rules, Formulas & Quick Tricks to Solve Trains Based Aptitude Problems

In this list of rules, you will get an idea that How to solve all different types & kinds of Trains based aptitude problems asked in various competitive exams like UPSC, SSC, Bank, and Railway examinations at all levels.

By using this method, you can able to solve all problems from basic level to advanced level of questions asked based on Trains in a faster approch.

Let's discuss the rules one by one with all Trains related formulas with examples,

RULE 1 :

If a train crosses an electric pole, a sitting/standing man, km or mile stone etc. then distance = Length of train. Then,

Length of train = Speed × Time

Time = $\text"Length of train"/\text"Speed"$

Speed = $\text"Length of train"/\text"Time"$


RULE 2 :

Let 'a' metre long train is going with the speed 'x' m/s and 'b' metre long train is also going with the speed 'y' m/s in the same direction on parallel path,then

Total time taken by the faster train to cross the slower train

$= {a + b}/{x - y}$ seconds


RULE 3 :

Let 'a' metre long train is travelling with the speed 'x' m/s and 'b' metre long train is travelling with the speed 'y' m/s in the opposite direction on parallel path.Then,

Time taken by the trains to cross each other

=${a + b}/{x + y}$ seconds.


RULE 4 :

If a train crosses a standing man/a pole in '$t_1$' sec time and crosses 'P' meter long platform in '$t_2$' sec. time, then

length of the train

= ${P × t_1}/{(t_2 - t_1)}$


RULE 5 :

Let 'a' metre long train is running with the speed 'x' m/s. A man is running in same direction and with the speed 'y' m/s, then

Time taken by the train to cross the man = $a/{(x - y)}$seconds.

And a = (x – y)t


RULE 6 :

Let 'a' metre long train is running with the speed 'x' m/s. A man is running in the opposite direction of train with the speed of 'y' m/s. Then,

Time taken by the train to cross the man = $a/{(x + y)}$ seconds.


RULE 7 :

A train crosses two men in $t_1$ seconds and $t_2$ seconds running in the same direction with the speed $s_1$ and $s_2$ then

The speed of train is = ${t_1S_1 - t_2S_2}/{t_1 – t_2}$

and length of train is l = $(S_1 - S_2)({t_1 - t_2}{t_1 - t_2})$


RULE 8 :

If two trains of (same lengths) are coming from same direction and cross a man in $t_1$ and $t_2$ seconds,then

Time taken by both the trains to cross each other

= ${2 × \text"Product of time"}/\text"Difference of time"$


RULE 9 :

If two trains of same length are coming from opposite directions and cross a man in t1 seconds and t2 seconds then

Time taken by both trains to cross each other

= ${2 × \text"Product of time"}/\text"Sum of time"$


RULE 10 :

If a train of length x m crosses a platform/tunnel/bridge of length y m with the speed u m/s in t seconds, then,

t = ${x + y}/u$


RULE 11 :

Two trains A and B, run from stations X to Y and from Y to X with the speed '$S_A$' and '$S_B$' respectively. After meeting with each other. A reached at Y after '$t_A$' time and B reached at X after '$t_B$' time. Then

Ratio of speeds of trains,

$S_A/S_B = √{t_B/t_A}$


RULE 12 :

If a train of length l m passes a bridge/platform of 'x' m in $t_1$ sec, then the time taken by the same train to cross another bridge/platform of length 'y' m is,

Time taken = $({l + y}/{l + x})t_1t$


RULE 13 :

From stations A and B, two trains start travelling towards each other at speeds a and b, respectively. When they meet each other, it was found that one train covers distance d more than that of another train.

The distance between stations A and B is given as

$({a + b}/{a - b}) × d$


RULE 14 :

The distance between two places A and B is x km. A train starts from A towards B at a speed of a km/hrr and after a gap of t hours another train with speed b km/hrr starts from B towards A, then both the trains will meet at a certain point after time T. Then, we have.

T = $({x ±tb}/{a + b})$

t is taken as positive if second train starts after first train and t is taken as negative if second train starts before the first train.


RULE 15 :

Excluding stoppage, the average speed of a train is u and with stoppage its average speed is v. Then,

The stoppage time per hour

= $\text"Difference between their average speed"/\text"Speed without stoppage"$

= ${u - v}/u$

With u > v and u, v ≠ 0


RULE 16 :

A train covers a distance between stations A and B in time $t_1$. If the speed is changed by S. then the time taken to cover the same distance is $t_2$. Then

The distance(D) between A and B is given by

D = S$({t_1t_2}/{t_1 - t_2})$ or $(S'/t')t_1t_2$

Where t' : change in the time taken


6 - Types of Trains Based Aptitude Questions and Answers Practise Test With Online Quiz

Click the below links & Learn the specific model from Trains problems that you have to practice for upcoming examination


Refer: Get all Topic-wsie Quantitative aptitude problems for upcoming competitive exams

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