Monday, 11 April 2016

[Q] Speed, Time & Distance Tricks - 1

Time and distance is a very easy topic and has limited variety of questions. I will take up questions from each variety and will solve them with shortest method possible.

Q. 1)

Let the distance travelled on foot be X km. Then distance travelled on bicycle will be Rs. (80 - X)
X/8 + (80 - X)/16 = 7
After forming this equation, don't solve it for X. Just observe, X/8 denotes that X is a multiple of 8 (although you can't be 100% sure, but SSC generally likes whole numbers). That means answer is either 32 km or 48 km.  Put X = 32 km in the equation and check if it satisfies the equation. It does!
Answer : (A)

Q. 2)

This is a commonly asked question. Just remember -
Time taken to cross a telephone pole = Time taken by the train to cover a distance equal to its length
Speed = 54 km/hr = 54 * 5/18 m/sec = 15 m/sec
Time taken by the train to cover a distance equal to its length = 300/15 = 20 sec
Answer : (A)

Q. 3)
If two objects A and B are moving at a given speed and we are asked "when will A overtake B" or "When will the police catch the thief", we use the concept of Relative Velocity. It's very simple

When the objects are moving in opposite direction, Relative velocity = Speed of A + Speed of B
When the objects are moving in the same direction, Relative velocity = Speed of A - Speed of B
Let the length of each train be L metres.
Here, the trains are moving in the same direction, hence relative velocity = Speed of train A - Speed of Train B = 10 km/hr = 10 * 5/18 m/sec = 25/9 m/sec
We know, Distance = Speed * Time
Here, Distance = Sum of the length of both the trains, i.e., 2L
Speed  = Relative velocity
Time  = Time taken by the faster train to overtake the slower train
So, 2L = 36 * 25/9
L = 50 m
Answer : (A)

Q. 4)

This question is similar to Q. No. 2. We just have to replace the Speed of the train, with Relative Velocity.
Let the length of the fast train be L.
Trains are running in the same direction, hence Relative Velocity = 40 - 20  = 20 km/hr = 50/9 m/sec
L = 50/9 * 5 = 250/9 metres
Answer : (C)

Q. 5)
You can solve such questions with two methods - 
Method 1 (Relative Velocity)
Relative velocity of A and B = 6 + 4 = 10 km/hr
They have to cover a distance to 20 km.
Hence they will meet in 20/10 = 2 hours
So if they start at 7 a.m., they will meet at 9:00 a.m.
Answer : (C)

Method 2 (Equate the distance)
Let A and B after t hours
Then distance covered by A in t hours + Distance covered by B in t hours = 20
t*4 + t*6 = 20
or t = 2 hours

Q. 6)

This question is similar to the above question. But it has a twist! The two trains are not moving at the same time. First train is starting at 7 am, while second train is starting at 8 am.
Method 1 (Relative Velocity)
Remember! To apply the relative velocity formula in such questions, we will first have to make the trains move at the same time. How?
Let the distance between the trains be X km
The first train takes 4 hours (7 am to 11 am) to move from A to B
Hence speed of the first train = X/4
The second train takes 3.5 hours (8 am to 11:30 am) to move from B to A
Hence speed of the second train = X/3.5
From 7 am to 8 am (1 hour), only the first train is moving. Distance travelled by the first train in 1 hour = X/4 * 1 = X/4
Distance left between the two trains = X - X/4 = (3/4)X
Relative velocity of the trains = X/4 + X/3.5
Time taken by the trains to cross one another = (Distance between them) / (Relative velocity)
= (3/4)X / (X/4 + X/3.5)
= 1.40 hours
= 1 hour 24 minutes
So the trains will cross one another at 8 am + 1 hr 24 min = 9 : 24 am
Answer (D)

Method 2 (Equate the distance)
Let the trains cross each other in t hours
First train starts early, so it will travel for complete t hours. But second train starts 1 hour after the first train, so it will travel for (t - 1) hours
Distance travelled by first train in t hours + Distance travelled by second train in (t - 1) hours = X
X/4 * t + X/3.5 * (t - 1) = X
t = 2.4 hours = 2 hours 24 minutes
But this time will be added to 7 a.m.
So, Answer = 7 a.m. + 2 hours 24 minutes = 9:24 a.m.

Q. 7)

This question is similar to the above question.
Chor-Sipahi questions are best tackled with Relative Velocity.
Relative Velocity of the Thief and the Owner = 50 - 40 = 10 km/hr
Distance travelled by the thief in half an hour (from 1:30 p.m. to 2 p.m.) = 0.5 * 40 = 20 km
Now the distance between the owner and the thief is 20 km.
So time taken to catch the thief = Distance between them / Relative velocity = 20/10 = 2 hours
He will catch the thief at 2 p.m. + 2 hours = 4 p.m.
Answer : (A)

Q. 8)

Method 1 (Relative velocity)
Let P and Q meet in t hours
Distance travelled by P in t hours = 20t (because the speed of P is 20 km/hr)
Distance travelled by Q in t hours = 30t (because the speed of Q is 30 km/hr)
Given, 30t - 20t = 36 km
or t = 3.6 hours
So P and Q meet after 3.6 hours
Relative velocity of P and Q = 20 + 30 = 50 km/hr
Distance between the two places = Time taken by P and Q to meet * Relative velocity = 50 * 3.6 = 180 km
Answer : (A)

Method 2
Let P and Q meet at point M. P has to travel X km to reach M and Q has to travel Y km.
Time taken by P to reach M = Time taken by Q to reach M
X/20 = Y/30
X/Y = 2/3
Given, Y - X = 36 km
Divide the whole equation with Y
1 - X/Y = 36/Y
1 - 2/3 = 36/Y  [Put X/Y = 2/3]
Y = 108 km
Hence X = Y - 36 = 72 km
Distance between the two places = X + Y = 108 + 72 km = 180 km
Answer : (A)

If you have any doubt in this article, please drop a comment.
Keep reading :)

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  1. q 1 can we solve with allegation method? then how....

    1. yes you I have explained in Mixture and Allegation Tricks - 2

  2. sir,how to solve TSD problems using LCM concept as we solve time and work problems?Also is there any shortcuts for boat and stream problems without any formula?

  3. Sir, how to solve this question using a simple method.
    If cos pie x=x^2-x+5/4, the value of x will be?

  4. Sir, your blog is proving to be extremely useful for us aspirants. Keep up the good work. Thank you.

  5. Sir from where to do science & technology part of general awareness for SSC CGL

  6. hello sir..please upload some more hack trick for reasoning sir ..your previous trick was awesome there any trick for series or missing number type question because it take too much time...upload some more lesson on reasoning sir ...

  7. This comment has been removed by the author.

  8. Q. two guns were fire the same place at an interval of 13 minute but a person but a person in a train hers second firing 12 min 30 sec after the first.. find the speed of train.. speed of sound - 330 m... sir plz isko smjha dena.. or is trh ke bahut qustn hai unme se koi achhe qutn bta dena

  9. And thnks sir mera score mock m 80 aara h... mujhe math thik thak aati h bt qutn nhi kr pata.. english errors m kbhi nhi krta.. sir 1 mnth m kya m grammar pdu ya math m dhyan du tali score at lest 115 tk aa jaye

    1. in my point of view you can just revise what u read in past month because cgl is about to come in next get 115 marks it's better to minimize your mistake instead of learn new thing this time..and do error question ..if you even not read grammer.. so do it atleat u can get 2 right in it so according to this u will get 2 marks for right and o.75 on wrong doing overall you will get 1.25 marks in error question my suggestion do it..

    2. This comment has been removed by the author.

    3. 1)practice old q.papers and note the techniques
      2)remember no sectional cutoff
      3)don't waste time in GK section. Either you know or Don't know

  10. Thank you so much brother.. Your tricks are always awesome... Please continue posting like this brother..ur tricks are really useful for all types of competitive exams.. Thank u so much.. Keeping sharing bro..

  11. Sir Apne Montex ka jo pen use kiya tha uska model please bata dijiye.

    1. ye wala-

  12. Sir Please Post Tricks to solve Trigonometry Question.

  13. Thanx sir... Plzz post some more tricks for trigno & algebra

  14. sir plzz post all tricks till Cgl-16 exam...really helpful

  15. Hello sir...i.have a doubt in, we took length of only the faster one...wht abt the length of the other...why should we ignore that length??

    1. Because the "faster train" is overtaking the man. The faster train has to cover the distance equal to its length to pass the man. We take the length of the train that "overtakes"

  16. Sir in q.8....y shouldn't we proceed by simply...d/50(30-20)=36...=>d=180km

    1. Dint get you....please elaborate...

    2. d/50 is the time where the both in that specific time diff of distance travelled by both is 36km...and so on

  17. Sir first of all, super awesome blog! Loved it! Totally amazing. Thanks for sharing so mucg stuff.
    Sir, hardly 4 weeks left, and i am doing fine in all sections except gs. Just started gs but lucent is too big. So i got that very thin essential manohar pandey. Can i get 10+ marks from that only? I'll be satisfied with tha.

    1. If you are finding Lucent bulky, just read history, polity and economics. These 3 topics and some common sense in science questions will surely fetch you 10+ marks. Good luck!

  18. 2.4 hours = 2 hours 24 minutes KAISE HUA SIR?

    1. 2.4 hours = 2 hours + 0.4 hours
      0.4 hours = 0.4*60 minutes = 24 minutes
      Hence 2.4 hours = 2 hours 24 minutes

  19. In Q.6) the expression 3/4X is a bit misleading can you make it (3/4)X or 3X/4.


  20. in Q.8) using relative velocity concept and ratio proportion concept, it takes 2 seconds

    10 --> 36
    50 --> ?

    i.e. if 10km/hr extra gives you a lead of 36, then 50km/hr(relative velocity) will give how much? I am not sure though if this is legit :P :D

  21. Hi prashanth sir I have dbt regarding 6th question y the adding time different for rel velocity n equate models finally when v get answer.Will u plz tell me y n for which train time v have to add the time.

  22. Hi prashanth sir I have dbt regarding 6th question y the adding time different for rel velocity n equate models finally when v get answer.Will u plz tell me y n for which train time v have to add the time.

  23. Hiii Prashant I too had dbt regarding 6th qsn abt adding please rectify our dbt

  24. Hi Sir,

    If two pipes can fill a cistern of capacity 1,00,000 liters in 20 hours and 30 hours respectively, find the time taken by both of them to fill 75,000 liters of water in it.

  25. Very useful blog. Sir please will u give some hacks for ibps reasoning puzzles... Egerousrly waiting for it...

  26. This comment has been removed by the author.

  27. Nice blog. Really helpful for when attending interviews crt training is most helpful…. If it possible share some more tutorials……….