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CAT 1994 | Question: 66

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2 2 votes

Shyam went from Delhi to Simla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Simla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Simla. If the average speed for the entire journey was 49 kmph, what was the average speed from Chandigarh to Simla?

  1. 39.2 kmph 
  2. 63 kmph 
  3. 42 kmph 
  4. None of these

1 Answer

0 0 votes

This is an example of non uniform motion with segments having uniform motion though.

So average speed is given by :

Average speed  =  Total distance / Total time

                              =  (d1 + d2 + d3 ....) / [(d1 / s1) + (d2/s2) ........]

Let  distance from Delhi to Chandigarh  =  (3/4)d

                    from Chandigarh to Simla  =  d  [ As mentioned in the question ]

      speed  from Delhi to Chandigarh    =   (1/2)s

                 from Chandigarh to Simla   =   s

Hence average speed                         =  [(3/4)d + d] / [{(3/4)d / (1/2)s} + (d/s)]

                                                         =  (7/4)d / [(3/2) + 1] (d/s)

                                                         =  (7/10)s

But given average speed for entire journey  =   49 kmph

Hence

        (7/10) s    =   49

==>   s            =   70   which is the same as average speed between Chandigarh to Shimla

Hence D) should be the correct answer.  

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