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

Aptitude70 Comments

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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.

  1. Visualizing the Concept: Train and Pen
  2. Case 1: One Train One Man (or Tree, Pole)
  3. Case 2: One Train One Platform (or bridge, tunnel)
  4. Case 3: Two Trains
  5. Unit Conversions
  6. 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
Flair writometer pen

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

TSD Train concept visualize

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?

Train and Platform

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 principle remains the same.

Case3: two trains crossing each other

Two trains are coming from opposite directions. Both of them are running at the same speed 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 less time 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 was zero, hence we took train’s speed as our final speed. But here second train is also moving so we’ve to consider it.

Alternative:

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

Here’s 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 will confidently 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 (60×60) 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.

Mrunal recommends

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  5. Spectrum: Modern History (Hindi | English)
  6. Bipin Chandra: Post Independence
  7. Fast-track to Arithmetic Rajesh Verma
  8. MK Pandey’s Analytical Reasoning
  9. Disha’s Topicwise Paperset (Hindi | English)
  10. School Atlas
  11. Mains: Language papers
  1. (free) NCERT, NIOS, TN-Books 4 History,Geo,Sci
  2. Indian Polity M.Laxmikanth (Hindi | English)
  3. Spectrum: Modern History (Hindi | English)
  4. Maths: Quantam CAT Sarvesh Kumar
  5. Objective General English SP Bakshi
  6. Word Power made Easy -Norman Lowe
  7. Topic wise Solved Paperset by Disha


So far 70 Comments posted

    1. Shikha

      thanks, really this is a good site.

      1. omi

        thank u shikha jee

    2. Vikas harit

      thanks for this

  1. RAGHAVENDRA

    THANK U

  2. dinesh

    hi i need the article for pipes and cistern,time and work and more example model in trainproblem ,, reply as soon as possible

  3. Manjunatha

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

    1. Jash

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

    2. sakthi

      even i got 710 . i think its correct.

  4. Ramya

    I too have a doubt on the case 3 problem. I have two queries when I go through problem on Trains.

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

    Here, when calculating the speed of the train, it was mentioned that 120/8. 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 will it pass a man who is running at 8kmph in the same direction in which the train is going?

    Please guide me in these two problems.

    1. Jacob Black

      Ramya,

      1) 120/8 because as compare to the train or plateform a man, telephone piller or such small items won’t matter, hence for calculating speed you’ve seen 120/8

      2) In this case you need to find the relative speed, when a man running in the same direction the train is going the relative speed will 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

    2. aman'z

      hey guys, can u tell me whats answer. .becoz, i think answer is 120m of train length and speed of train is 15 m/sec

  5. harideep

    Hello sir,Which authors vedic mathematics book i.e, for speed maths will be good?

  6. SATRAJIT CHAKROBORTY

    please give some shortcuts on data interpretation for sbi p.o.

  7. shruthi

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

  8. Lake.Chaitanya kumar

    solve this question please

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

      1. Lake.Chaitanya kumar

        thank you mrunal sir

    1. Praveer Parmar

      Answer is 15 minutes

  9. gourav sharma

    please tell me the answer of case 3 ..i’m getting 710 …please correct me if i’m wrong..!!!!!!!

  10. ABHA RANI

    DOING A GR8 JOB REALLY!!!! A TRUE INSPIRATION N A GENUINE HUMAN BEING AND AN EPITOME GENEROSITY.ITS MY MAIDEN VISIT TO UR WEBSITE N M REALLY IMPRESSED SIR…

  11. Shikha

    if two trains are moving in the direction facing each other or facing opposite to each other or moving straight with each other, then what different techniques can be used?

    1. Mrunal

      relative speed concepts for trains
      if two trains moving in same direction (like in racing)=bigger minus smaller speed
      if two trains moving in opposite direction=bigger plus smaller speed
      if two trains moving away from each other=bigger plus smaller speed

  12. VISHNU

    A train crosses a pole in 15 seconds, while it crosses 100 meter long platform in 25 seconds. The
    length of the train is –
    a. 125m
    b. 135 m
    c. 159 m
    d. 175 m

    can u solve this problem sir ?

    1. Mrunal

      if speed of train is “s” and length of train is “d”
      when crossing pole
      s x 15=d
      when crossing platform
      s x 25 =(d+100)

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

      1. chetan

        ans is 150 metre
        as speed = distance of train/time to cross pole and also speed = (distance of train+platform distance)/time to cross the pole.
        So,d/15=(d+100)/25

  13. Mudasir

    A 280m long train ,travelling at a uniform speed,crosses a platform in 60sec and a man standing on the platform in 20sec.whats the length of the platform?

    1. sandeep

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

      So, x = 560 m

  14. Akshat Sharma

    Sir, Pls upload some material and tricks on reasoning. It is a most time consuming section for us in SSC CGl. Thanks in advance.

  15. VimalDeshmukh

    in second case if a man and train running in the same direction any changes in solving method?

  16. VimalDeshmukh

    A train 123 m long passes a man, running at speed 5km/hr in the same direction, 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 this case i have to calculate relative speed for which i have minus bigger speed from smaller speed.. but i don’t know how to solve after that..

  17. sandeeep

    A train X leaves Howrah at 6 a.m. and reaches Asansol at 10 a.m. Another train Y leaves Asansol at 8 a.m. and reaches Howrah at 11.30 a.m. then the two trains cross one another at
    can anyone help??

  18. sandeeep

    A train X leaves Howrah at 6 a.m. and reaches Asansol at 10 a.m. Another train Y leaves Asansol at 8 a.m. and reaches Howrah at 11.30 a.m. then the two trains cross one another at
    can anyone help me ?

    1. deepak kumar

      ans is 8:56am

  19. MNAISH AVASTHI

    THIS IS THE GOOD WAY TO UNDERSTAND THE BASIC

  20. vishal

    The driver of a maruti car driving at a speed of 68km/h locates a bus 40m ahead of him. After 10sec the bus is 60m behind. The speed of the bus is
    A.30km/h
    B.32km/h
    C.25km/h
    D.38km/h
    Solve it….

    1. Nalina

      This involves the concept of relative speed:
      let the speed of the bus be x m/s
      speed of the car = 68km/hr (or) 170/9 m/s
      in 10s the car covers a distance of 100m(40 + 60) at a speed of (170/9 – x)m/s
      distance = speed*time
      100 = (170/9 -x) *10
      x = 80/9 m/s
      now convert it to km/hr which is 32 km/hr
      ans is B

  21. vishal

    The driver of a maruti car driving at a speed of 68km/h locates a bus 40m ahead of him. After 10sec the bus is 60m behind. The speed of the bus is
    A.30km/h
    B.32km/h
    C.25km/h
    D.38km/h
    Solve it..

  22. vishal

    (1) train a and b are travelling on the same route heading towards the same destination. Train b has already covered a distance of 220km before 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 of 220 km) they would met after an hour.
    Q.what is the speed of train a in kmph
    A.102
    B.118
    C.81
    D.none
    Q. What is the speed of train b in kmph
    A.150
    B.136
    C.100
    D.120
    Help me wid it..

  23. Abhay

    Sir, please provide a solution for this question:

    A man standing on a railway platform notices that a train going in one direction takes 10 seconds to pass him and other train of the same length takes 15 seconds to pass him. Find the time taken by the two trains to cross each other when they are running in the opposite directions.

    1. omprakash B

      Let 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

      1. omprakash B

        Take D1=D2=D as mentioned in the given data

        1. omprakash B

          sorry……..
          Typo at the 4th line from the bottom
          T=({V1 x 10} +{V2 x 15}) / (V1’+’V2)

  24. Gentleman Raju

    You, sir, are an incarnation of Plato. A genius endowed with great imagination. Thanks a lot. *sob* *sob*

  25. NIMESH PATEL

    thank you so much sir….

  26. NIMESH PATEL

    It is very easy solution.Thank you so much sir.

  27. ganesh

    A passenger in train P travelling at 1km/min uses his stop watch and finds that another train Q travelling in opposite direction, completely passed his window in 3sec. If the length of train Q is 87.50m. find its speed?

    1. Sasikumar

      Ans: Velocity of Q is 12.5 m/s or 45 kmph
      P travels at 60kmph or 50/3 m/s
      Q travels at 87.5/3 m/s
      As per Relative velocity, Velocity of Q – Velocity of P = required answer

  28. santosh kumar prajapati

    2sin(πx/2)=x2 +1/x2
    Then what is value of the (x – 1/x)

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

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

  30. shruthi

    Local trains leave from a station at an interval of 15minutes at a speed of 16km/hr.A man moving from opposite side meets the trains at an interval of 12 minutes.The speed of the man is :

    Plz anyone tell me the solution

    1. kalyan

      could you plz send me the any imp topic material sruthi..

  31. Nina

    A goods trains of length 600 meters traveling at a uniform speed completely passes the platform of a station 45 seconds. If the

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

    1. ANITHADEVI

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

      speed =distance/time
      s =900m/45sec = 20m/sec
      convert into km/hr so multiply by 18/5
      20*18/5 =72km/hr is the answer……

  32. SANTHOSH S K

    Sir, How to solve these using STD table?

    A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train 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 in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?

  33. surbhi

    a train is running with d speed of 93km,another train with speed of 51 km coimng from opposite side and crosses each other in 24 seconds. the train crosses a bridge in 66 seconds then length of bridge in meters is?

    plz solve dis…

  34. Zeeshan Khan

    My first visit to mrunal.org and I found it so damn impressive.

  35. ashadeepthi

    a person going in a cae at 30kmph reches t1minutes late, if he goes at 40kmph he reaches the office t2 minutes early. find the distance between the office and his house

  36. kalyan

    hi sir or medam
    any body can you plz send me all type of rrb material or railway jobs matreial on most important topics..
    on given my below id.
    at least few material also send me sir..or medam

  37. Amit shukla

    एक ट्रेन x से शहर y की तरफ़ जाते हुए 1 घंटे बाद दुर्घटना ग्रस्त हो जाने पर इसे आधा घंटा रोक लिया जाता है. इसके बाद यह अपनी सामान्य चाल की 4/5 चाल से चलकर y पर 2 घंटे देरी सि पहुँचती है. यदि दुर्घटना से पहले 80 km चली होती तो केवल 1 घंटे. देरी से पहुँचती.दुर्घटना सि पहले ट्रेन की चाल बताओ.तथा उंकि बीच की दूरी क्या है

  38. chetna ramesh Lalwani

    Yes I too got 710.

  39. rahul

    A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 kmph in 33 seconds. The speed of the train is:
    please solve it

  40. virat kohli

    A train after travelling 50 km from A meets with an accident and proceeds at 4/5th of former speed and reach B 45 mins late.Had accident happened 20 km further on,it would arrive 12 min sooner.Find original speed and distance?

  41. pooja soni

    Can u please suggest a good book for quant

  42. mounika

    The driver of a car driving @376km/hr locates a bus 40meters ahead of him .after 20secs the bus is 60meters behind .the speed of the bus is.

  43. Jassa

    The two train are travel in the same direction at 56K.M and 29K.M an hour and the faster train passes a man in the slower train in 16 seconds. Find the lenth of faster train.
    A. 120M
    B. 150M
    C. 140M
    D. 100M.
    Please tell me how did we solve it

    1. iamanswer

      relative speed 56-29 = 27kmph = 7.5mps( so man is static now= take him as a point)
      train crosses that point in 16 sec with speed 7.5 mps , so distance traveled by train is it’s length
      d=sxt = 7.5*16=120meter

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