Aptitude (http://mrunal.org/category/aptitude) / 3 years Ago /55 Comments (http://mrunal.org/2012/03/aptitude-trains-platforms-tsd.html#comments)

Main-Topic: Time, Speed Distance (TSD)

Subtopic: Trains and Platforms.

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

1. Visualizing the Concept: Train and Pen2. Case 1: One Train One Man (or Tree, Pole)3. Case 2: One Train One Platform (or bridge, tunnel)4. Case 3: Two Trains5. Unit Conversions6. Previous Articles on Aptitude

Visulize: Pen and Train

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

You must have seen the advertizement of a ballpen Flair Writometer. They claim it can writefor 2,500 metres and even provide a marking scale on the ballpen refill to measure thedistance! See the photo

(http://img543.imageshack.us/i/flairwritormeterpen.jpg/)

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

English: SP Bakshi(http://www.flipkart.com/objective-general-

english-2012/p/itmdyuqqgafhtehp?pid=9788183480000&affid=mrunalrugm)

Mrunal (http://mrunal.org/)

So Youre standing on a Railway platform, holding that writometer pen in your hand, pointing itstraight towards the upcoming trains side, like this photo

(http://img338.imageshack.us/i/trainconceptvisual.png/)

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

Now you open the pens refill and check the markings, obviously few mili-litres of ink is used andmarking would show that youve 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 helda writometer pen in his hand pointing it out of the window and towards the platform.So as thetrain passed, his pen also drew a straight line on the entire platform. Later he checks the refill ofhis 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 persecond, crosses a man in 10 seconds. What is the length ofthe train?

For all the problems about train, boats, cars, scooters, men required to complete a job, tatanano and kingfisher airplane, in short TSDW (time,speed, distance, work) you need to rememberonly 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 youin 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 arailway platform in 20 seconds. If the length of the train is100 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 therailway also holding a purple pen.

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

(http://img805.imageshack.us/i/caseonetrainoneplatform.png/)

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

So apply the STD formula

s x t = D

20ms x 20 seconds = (100+x)

400m = 100+x

x=400-100

x=300m

Final answer: length of this platform is 300 metres.

Alternative: instead of railway platform, they can use the word Bridge, Tunnel but the principleremains the same.

Case3: two trains crossing each other

Two trains are coming from opposite directions. Both of them are running at the samespeed 20 meter per second.

It takes 20 seconds for them to completely cross each other. If the length of first train is 90 m,what is the length of the second train?Visualise: you are holding a pen sitting in first train, I am holding a pen sitting in the second.

The total length of line drawn is 90+x m

Since both of the trains are moving, and moving in opposite directions. Meaning it will take lesstime to draw these lines.

Hence

Final speed (s)

= speed of first train+ speed of second train.

= 20+20

= 40 m/s

Now it can be solved just like the case #2.

In the case #1 and #2, Man and Platform were stationary (unmoving) objects so their speed waszero, hence we took trains speed as our final speed. But here second train is also moving soweve to consider it.

Alternative:

same question, but instead of two trains , it is one man riding on a bike and another traincoming from the opposite direction.

Heres the length of length of line

=Line drawn on Train + Line drawn on Bike

= 90m +zero meter. (because length of bike is negligible, we take it zero)

So Distance (d)= 90.

but for the speed we have to add

=Train + Bike

=20+20

S=40 m/s

After that, principle remains the same as Case #3

Unit conversions

It is essential that before applying the STD formula, all the unit is must be in the same system,else you will get incorrect answer.

and they will give that incorrect answer in one of the four options [a/b/c/d] so you willconfidently tick it but end up loosing in negative marking.

So in the STD formula. Everything must be

either in meter,second,

or in kilometer, hour.

Remember

1 km per hour = 5/18 meter per second.

How did we derive this?

1 kilometer per hour

=1000 meters per 60 minutes

=1000 meters per (6060) seconds

=1000 meters per 3600 seconds

=10 meters per 36 seconds (cut the zeros)

=5 meters per 18 seconds. (half of 10 and 36)Meaning

if a train is running a 36 kms per hour then, its speed in meter per second is:

1 kmph = 5/18 ms

36 kmph= 36x (5/18) = 10 m/s.

If the reverse is asked, (10 m/s then how much in kmph?),

simply multiply with reverse 18/5, because

5/18 ms = 1 kmph

1 ms= 18/5 kmph

10 ms= 10 x (18/5) kmph = 36 kmph.

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syed waseem pashaSmall suggestion :- for those of Fellow Aspirants having internet they cansolve aptitude/reasoning questions, there is a good website

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Shikha

Shikhathanks, really this is a good site.

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omithank u shikha jee

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dineshhi i need the article for pipes and cistern,time and work and moreexample model in trainproblem ,, reply as soon as possible

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Anuraghttp://www.indiabix.com/aptitude/questions-and-answers/(http://www.indiabix.com/aptitude/questions-and-answers/)Link contain all RS Agarwal, questions

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Manjunatha

What is the answer for case-3 problem??Is it 710..i.e (90+x = 40*20)?

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JashEvn i gt 710. Bt i m nt sure whether it is right or wrong???

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RamyaI too have a doubt on the case 3 problem. I have two queries when I gothrough problem on Trains.

1. The problem is A man is standing on a railway bridge which is 180 mlong. He finds that a train crosses the bridge in 20 sec but himself in 8sec. Find the length of the train and its speed.

Here, when calculating the speed of the train, it was mentioned that120/8. Y 8 alone. why the 20 sec is not there instead of 8?

2. A train 150m long is running with a speed of 68kmph. In what time willit pass a man who is running at 8kmph in the same direction in which thetrain is going?

Please guide me in these two problems.

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Jacob Black

Ramya,

1) 120/8 because as compare to the train or plateform a man,telephone piller or such small items wont matter, hence forcalculating speed youve seen 120/8

2) In this case you need to find the relative speed, when a manrunning in the same direction the train is going the relative speedwill be the difference of both, i.e.

Relative Speed= 68-8 = 60KMPH = 60*5/18 = 50/3 Mtr/Sec

as you know S=D/T or T=D/S => 150/(50/3)= (150*3)/50 = 9 Second

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aman'zhey guys, can u tell me whats answer. .becoz, i think answer is120m of train length and speed of train is 15 m/sec

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harideepHello sir,Which authors vedic mathematics book i.e, for speed maths willbe good?

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SATRAJIT CHAKROBORTYplease give some shortcuts on data interpretation for sbi p.o.

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shruthinice

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shruthijust try place some more examples on trains concept in different ways

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Lake.Chaitanya kumarsolve this question please

walking 5/7 of his usual rate a boy reaches his school 6 min late.find hisusual time to reach the school?

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Mrunal (http://mrunal.org)concept is already explained in another article. checkhttp://www.mrunal.org/aptitude (http://www.mrunal.org/aptitude)

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Lake.Chaitanya kumarthank you mrunal sir

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Praveer ParmarAnswer is 15 minutes

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gourav sharmaplease tell me the answer of case 3 ..im getting 710 please correct meif im wrong..!!!!!!!

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ABHA RANIDOING A GR8 JOB REALLY!!!! A TRUE INSPIRATION N A GENUINE HUMANBEING AND AN EPITOME GENEROSITY.ITS MY MAIDEN VISIT TO URWEBSITE N M REALLY IMPRESSED SIR

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Shikhaif two trains are moving in the direction facing each other or facingopposite to each other or moving straight with each other, then whatdifferent techniques can be used?

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Mrunal (http://mrunal.org)

relative speed concepts for trainsif two trains moving in same direction (like in racing)=bigger minussmaller speedif two trains moving in opposite direction=bigger plus smallerspeedif two trains moving away from each other=bigger plus smallerspeed

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Shikhathanks sir

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VISHNUA train crosses a pole in 15 seconds, while it crosses 100 meter longplatform in 25 seconds. Thelength of the train is a. 125mb. 135 mc. 159 md. 175 m

can u solve this problem sir ?

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Mrunal (http://mrunal.org)

if speed of train is s and length of train is dwhen crossing poles x 15=dwhen crossing platforms x 25 =(d+100)

divide eq.1 by 2, s will cancel and you get value of d.

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chetanans is 150 metreas speed = distance of train/time to cross pole and alsospeed = (distance of train+platform distance)/time to crossthe pole.So,d/15=(d+100)/25

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MudasirA 280m long train ,travelling at a uniform speed,crosses a platform in60sec and a man standing on the platform in 20sec.whats the length ofthe platform?

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sandeep(280+x)/60 = 280/20Where x is length of platform.

So, x = 560 m

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 1 4 0 8 6 4 # R E S P O N D )

Akshat SharmaSir, Pls upload some material and tricks on reasoning. It is a most timeconsuming section for us in SSC CGl. Thanks in advance.

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VimalDeshmukhin second case if a man and train running in the same direction anychanges in solving method?

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VimalDeshmukhA train 123 m long passes a man, running at speed 5km/hr in the samedirection, in the train is going, in 10 seconds. The speed of the train is:-A)45 km/hr B)50 km/hr C)54 km/hr D)55 km/hr. .. i know that, in thiscase i have to calculate relative speed for which i have minus biggerspeed from smaller speed.. but i dont know how to solve after that..

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sandeeepA train X leaves Howrah at 6 a.m. and reaches Asansol at 10 a.m. Anothertrain Y leaves Asansol at 8 a.m. and reaches Howrah at 11.30 a.m. thenthe two trains cross one another atcan anyone help??

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sandeeepA train X leaves Howrah at 6 a.m. and reaches Asansol at 10 a.m. Anothertrain Y leaves Asansol at 8 a.m. and reaches Howrah at 11.30 a.m. thenthe two trains cross one another atcan anyone help me ?

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ?R E P L Y T O C O M = 2 9 0 3 2 3 # R E S P O N D )

deepak kumarans is 8:56am

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 1 4 8 0 8 7 # R E S P O N D )

MNAISH AVASTHITHIS IS THE GOOD WAY TO UNDERSTAND THE BASIC

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vishalThe driver of a maruti car driving at a speed of 68km/h locates a bus 40mahead of him. After 10sec the bus is 60m behind. The speed of the bus isA.30km/hB.32km/hC.25km/hD.38km/hSolve it.

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ?R E P L Y T O C O M = 2 1 0 4 2 4 # R E S P O N D )

NalinaThis involves the concept of relative speed:let the speed of the bus be x m/sspeed of the car = 68km/hr (or) 170/9 m/sin 10s the car covers a distance of 100m(40 + 60) at a speed of(170/9 x)m/sdistance = speed*time100 = (170/9 -x) *10x = 80/9 m/snow convert it to km/hr which is 32 km/hrans is B

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 1 5 2 0 7 8 # R E S P O N D )

vishalThe driver of a maruti car driving at a speed of 68km/h locates a bus 40mahead of him. After 10sec the bus is 60m behind. The speed of the bus isA.30km/hB.32km/hC.25km/hD.38km/hSolve it..

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 1 5 2 1 3 1 # R E S P O N D )

vishal(1) train a and b are travelling on the same route heading towards thesame destination. Train b has already covered a distance of 220kmbefore train a started.

(2) the two trains meet each other 11hours after the start of train a.(3) had the trains been travelling towards each other (from a distance of220 km) they would met after an hour.Q.what is the speed of train a in kmphA.102B.118C.81D.noneQ. What is the speed of train b in kmphA.150B.136C.100D.120Help me wid it..

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AbhaySir, please provide a solution for this question:

A man standing on a railway platform notices that a train going in onedirection takes 10 seconds to pass him and other train of the samelength takes 15 seconds to pass him. Find the time taken by the twotrains to cross each other when they are running in the oppositedirections.

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ?R E P L Y T O C O M = 2 8 2 7 6 8 # R E S P O N D )

omprakash BLet Train length= D meters

length of first train is D1= V1 x 10 (1)

length of second train is D2= V2 x 15.(2)

equation (1)/equation(2)

Therefore,

V1/V2=15/10=3/2(3)

Time taken by two trains to cross each other is :T = (D1+D2) / (V1+V2).(4)

= ({V1 x 10} +{V2 x 15}) / (V1/V2)

divide numerator and denominator by V1

equate the values for V2/V1 from equation (3)

=12 seconds

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ?R E P L Y T O C O M = 2 8 2 7 6 9 # R E S P O N D )

omprakash BTake D1=D2=D as mentioned in the given data

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ?R E P L Y T O C O M = 2 8 2 7 7 2 # R E S P O N D )

omprakash B

sorry..Typo at the 4th line from the bottomT=({V1 x 10} +{V2 x 15}) / (V1+V2)

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 2 0 1 1 6 1 # R E S P O N D )

Gentleman RajuYou, sir, are an incarnation of Plato. A genius endowed with greatimagination. Thanks a lot. *sob* *sob*

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 2 0 2 1 9 2 # R E S P O N D )

NIMESH PATELthank you so much sir.

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 2 0 2 1 9 3 # R E S P O N D )

NIMESH PATELIt is very easy solution.Thank you so much sir.

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 2 1 2 9 8 7 # R E S P O N D )

ganeshA passenger in train P travelling at 1km/min uses his stop watch andfinds that another train Q travelling in opposite direction, completelypassed his window in 3sec. If the length of train Q is 87.50m. find itsspeed?

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ?

R E P L Y T O C O M = 2 3 6 0 0 1 # R E S P O N D )

SasikumarAns: Velocity of Q is 12.5 m/s or 45 kmphP travels at 60kmph or 50/3 m/sQ travels at 87.5/3 m/sAs per Relative velocity, Velocity of Q Velocity of P = requiredanswer

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 2 4 9 9 1 5 # R E S P O N D )

santosh kumar prajapati2sin(x/2)=x2 +1/x2Then what is value of the (x 1/x)

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 2 9 4 1 6 1 # R E S P O N D )

if two trains are crossing each other and plateformlength is given like 1 km and train' s length is notmentioned and speed for both trains are as 40 km/ hrand 50 km/ hr respectively..could anyone please tell meit' s valid answer which can satisfy allif two trains are crossing each other and plateform length is given like 1km and train s length is not mentioned and speed for both trains are as40 km/ hr and 50 km/ hr respectively..could anyone please tell me it svalid answer which can satisfy all the conditions

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 3 0 3 5 6 0 # R E S P O N D )

shruthi

Local trains leave from a station at an interval of 15minutes at a speed of16km/hr.A man moving from opposite side meets the trains at aninterval of 12 minutes.The speed of the man is :

Plz anyone tell me the solution

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 3 0 6 0 2 0 # R E S P O N D )

NinaA goods trains of length 600 meters traveling at a uniform speedcompletely passes the platform of a station 45 seconds. If the

length of platforms is 300 meters. Find the speed of the train inkilometers per hour?

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ?R E P L Y T O C O M = 3 3 8 7 7 6 # R E S P O N D )

ANITHADEVIgiven that length of both the train and platform are 600 and 300m.so the distance is 600+300 =900mtrain passes platform 45sec. so time also given, we have to findspeed of train in km/hr?

speed =distance/times =900m/45sec = 20m/secconvert into km/hr so multiply by 18/520*18/5 =72km/hr is the answer

R E P L Y ( / 2 0 1 2 / 0 3 / A P T I T U D E - T R A I N S - P L A T F O R M S - T S D . H T M L ? R E P L Y T O C O M = 3 3 5 7 0 7 # R E S P O N D )

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Sir, How to solve these using STD table?

A train overtakes two persons walking along a railway track. The first onewalks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4and 8.5 seconds respectively to overtake them. What is the speed of thetrain if both the persons are walking in the same direction as the train?

A train overtakes two persons who are walking in the same direction inwhich the train is going, at the rate of 2 kmph and 4 kmph and passesthem completely in 9 and 10 seconds respectively. The length of the trainis?

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