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Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Total Gadha - Thursday, 23 November 2006, 06:43 AM
 

Here is a textbook situation in Time, Speed and Distance: A man goes from point A to point B with velocity v1 and returns with velocity v2. What is his average velocity?

Using the formula image, the average velocity can be found to be image. So far so good.

Ever wondered why we get this result? Why do we get the velocity as the harmonic mean of the two velocities? The answer lies in basics of arithmetic and harmonic progressions.

Let t1 and t2 be the time taken while going from A to B and coming back. The situation is shown below:

image

Now what will a hypothetical average velocity in this situation mean? It will mean that a person takes the same time, taverage, while going from A to B and coming back. The situation is summarized below:

image

The total time taken will be same as t1 + t2

--> 2 × taverage = t1 + t2 or taverage = (t1 + t2)/2

In another words, t1, taverage, and t2 will be in arithmetic progression.

So how is this related to velocity?

Remember that when distance is constant velocity is inversely proportional to time?

I.e. V is proportional to 1/T or V = k/T.

If T1, T2, and T3 were in arithmetic progression, then 1/T1, 1/T2, 1/T3 are in harmonic progression => k/T1, k/T2, k/T3 are in harmonic progression => V1, V2 and V3 are in harmonic progression!

It can also be proved that if V1, V2 and V3 are in arithmetic progression, then T1, T2, and T3 are in harmonic progression.

So here’s the rule:-

 image

Now let’s apply these rules in practical problems:-

image

image

image

image

image

 

I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

 

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Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by rmmozhi prathiba - Tuesday, 8 May 2007, 11:20 PM
  A and S walk up an escalator. The escalator moves at a constant speed A takes 9 steps for every 16 of S's steps. A gets to the top of the escalator after having taken 30 steps while S, because of his faster pace, ends up taking 40 steps to reach the top. If the escalator was turned off, how many steps wud they have to take to walk up? how to answer this tg??? help me plz..
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Total Gadha - Wednesday, 9 May 2007, 03:09 AM
  quant lessons arithmetic geometric progression time speed distance
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by rmmozhi prathiba - Tuesday, 15 May 2007, 09:28 PM
  Thank you tg.. sorry for the delayed response i had a problem wth the net.. thank you.. this section was superb.. i will post you more and more doubts smile
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by gunjan bhargava - Thursday, 2 August 2007, 02:43 PM
 

Hi TG,

        i found ur approach really superb .nw i cn solve dese probs in few seconds.thanku so much 4 .u rock dude.

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Akon Convict - Friday, 3 August 2007, 09:50 AM
  Great TG
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by parag kumar - Friday, 24 August 2007, 02:02 PM
 

Quite simply outstanding ! Questions on still water, upstream and downstream flow look too easy after reading this. Thanks.

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Arun Prasad G - Saturday, 25 August 2007, 12:04 PM
 

TG,

Everything sounds fine and the method is impressive. Thanky you very much.

For question number 4, we get 72 and 21 as the two different roots of the equation. You took 72. Can you explain why?

 

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by shyam Sundar - Monday, 10 September 2007, 08:19 PM
 

TG

 

Ur concept of speed and time being in AP and HP was stupendous !!

Bow to you !!!

In every cat , we find that we can solve  a lot of qns by the use of these indirect methods or subtle tricks as we may call them .

 

May i kindly request you to provide all such tricks at once place so that students would benefit a great deal . I know this is tough , but its just a request from me !!

 

Anyway U Rock !!!!

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Nidhi Chopra - Friday, 14 September 2007, 03:13 PM
 

Ans to 5th part is 40 min..

Plz tell if it is correct..

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by rohit avasthi - Tuesday, 18 September 2007, 02:20 PM
  gr8 article.....thnx a lot TG....
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by naga kiran kosuru - Tuesday, 16 October 2007, 03:06 PM
 

hi TG

For question number 4, we get 72 and 21 as the two different roots of the equation. You took 72. Can you explain why?

 

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by RIDHIMA CHOPRA - Thursday, 25 October 2007, 11:32 PM
 

thanx a ton tg

ur simply great!!!!!!!!!!!!

plz give some more probs for practice

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by gayatri kumari pati - Wednesday, 14 November 2007, 09:32 PM
  thanq so much for description of these solutions.thanq so much
5th problems ans is 40
tell me is it right
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Sandy Kang - Saturday, 26 July 2008, 11:46 PM
  Simply Awesome , you are the Best Donkey after the one in Shrek smile
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by lipsa samantaray - Friday, 1 August 2008, 09:57 AM
 

Hi TG,

Please explain this solution once again..m able to get you but i have a doubt

 

Will the time taken for both of them to cross the same number of steps be equal......pls explain.B will take less time to climp up the elevator than A.

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by peeyush goela - Monday, 6 October 2008, 09:57 PM
  i think the answer to 5th question will be 45
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by kunal gulati - Wednesday, 15 October 2008, 09:53 PM
  no.. its 40........ harmonic mean of 30 and 60 ...
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Ram Sharma - Wednesday, 5 November 2008, 12:36 AM
  Gr8 Article TG..   U Rock!!!!
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Swayam Prabha - Wednesday, 5 November 2008, 01:59 AM
 

Hey Tg,

After this article things look easy....

Thanx!!!

 

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Ram Sharma - Thursday, 13 November 2008, 12:53 PM
  The ans. to the last problem would be 40 i.e. the HM of 30 ans 60.... Temme TG, Is that correct????
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Ram Sharma - Thursday, 13 November 2008, 12:55 PM
 

It would be nice if u cud come up with more of such tricks.... These will really add to our armoury for CAT....

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by alsadra @TG - Monday, 2 February 2009, 06:57 PM
  Hi naga, the answer to Qn no. 4 is either or 12. so u make take 72 as well as 21 as the value for x.


with regards
Alosies
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by abhishek sarkar - Saturday, 15 August 2009, 09:36 PM
  Hey TG.Thanx for the wonderful concepts.
Can You solve 1 problem i am having difficulty with?
Qs>
A bird flies a certain distance against the wind in 9 hrs more time than it takes to fly with the wind.
The bird doubles its speed. Then it takes 1.5 hrs more  to fly the same distance against the wind than it takes to fly with the wind. Find the speed of the bird?
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by HARSHAL KULKARNI - Tuesday, 15 November 2011, 08:26 PM
 

I didnt find this simple concept explained anywhere else. I have surely read some books and referred some sites for TSD, but the Fundas given by yoy are just awesome. I had never thought that problems of boat-upstream-downstream could be solved orally..

Hats off to TG

Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by Sharad Jain - Saturday, 18 January 2014, 06:41 PM
  In the Fourth Question, I too Was Wondering About the other root. ( t =21 ) wide eyes

TG, Why You haven't considered the the other root?
Re: Quant Exotica- Use of Arithmetic and Harmonic Progressions in Time, Speed, and Distance
by satish reddy - Friday, 31 January 2014, 04:24 PM
 

hi TG

U r aricle is awesome.