16 thoughts on “Weighted Averages – CAT Scan

    • Dear J
      My mind got sea saw feeling after reading explanation. kindly provide alternative solution if possible in reply.

      • This was an alternative solution only. The normal solution could be by using regular weighted averages, or by creating equations. That you can find in several places online.


  1. Dear J,
    This application using graphs was not very intuitive for me (personally) 😦 . Although you told that the ratio of their bases will govern their weights, but i’m just accepting it as it is, coz i’m not a fairly acquainted with this graphing technique 😦 . Can we some more questions and/or articles where we can learn these graphing techniques along with other concepts? I’ll be indebted if do so.

    • This was more of Geometry really (similarity of triangles!)…I don’t really have any similar questions but am trying to come up with a set of posts on graphing approaches in general (mods/quadratics etc), so far don’t have a coherent plan in place for that. It is surprisingly difficult to explain on paper, it turns out….


      • Dear J,
        Other graphing techniques are fine like drawing a graph for MOD(2x-3), but I meant graphing where in we have to picturize some data (like the example above) rather than an algebraic expression. Percentage of B v/s C on a horizontal line (how does it come to mind). I want to learn that. 😦 Please do something.

  2. Sir, I have a doubt. I started trying without goin thru solution first.

    as Shabnam can fully utilize or partially utilize…. I assumed w1,w2 and w3 as weights. I end up with the equation: (w1*0.1% + w2*1% – w3*0.25%) / (w1+w2+w3). [I assumed 50% probability for rise and fall of market].

    So I thought, in the numerator if I equalize the first term and the second term, I ll get the more return. Equalizing I found, w1:w2 :: 25:1, from this I got the total return as 0.78%.

    I know my approach is wrong, If you could point out where it is.


    • The second weightage should be either 1 or 0. Either invest fully in that option or not at all 🙂 Because that is a “guaranteed return”. The others are changing and hence a combination of them might make more sense (this being a simplified version of what the Finance folks call hedging)


  3. Sir,
    Could one try to solve such a question in a different way, i.e., instead of using the graphing technique. I tried to, but, couldn’t get my head around it.
    Thank You

    • Of course! You can solve it with equations as well (in fact that is how I solved this problem the first time I saw it – it is slightly slower but I didn’t spot this approach on that day!). The thing is, there will always be many ways to solve any given question; the more you know, the more likely you are to spot an efficient way to get an accurate answer.


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