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Math Help - Aunti's Share!

  1. #1
    Newbie andro45's Avatar
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    Unhappy Aunti's Share!

    here is a puzzle from Shakuntala Devi's:

    When my uncle in Madura died recently, he left a will, instructing his
    executors to dividehis estate of Rs 1,920,000 in this manner:
    Every son sould receive three times as much as a daughter, and that every
    daughter should get twice as much as their mother. What is my aunt's share?

    the answer is mentioned like this:


    -----------------------------------
    can anyone get the answer!!!!?
    i've asked many ppl, but nobody solved it!
    please HELP!
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  2. #2
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    Hello, andro45!

    I explained this at another site.
    Some information is missing . . . and the given answer is wrong!


    When my uncle died recently, he left a will, instructing his executors
    to divide his estate of $1,920,000 in this manner:

    Every son sould receive three times as much as a daughter,
    and that every daughter should get twice as much as their mother.

    What is my aunt's share?

    The answer is: . 49200\frac{10}{13} . Impossible!

    Let  x = the mother's share.
    Then  2x = each daughter's share.
    And  6x = each son's share.

    Let  S = number of sons.
    . . They will receive 6Sx dollars.

    Let  D = number of daughters.
    . . They will receive 2Dx dollars.

    Their mother will receive x dollars.

    Hence: . 6Sx + 2Dx + x \;=\;1,\!920,\!000


    And we have: . (6S + 2D + 1)x \;=\;1,\!920,\1000 .[1]



    If x \:=\:49,200\frac{10}{13} \:=\:\dfrac{639,610}{13} is the answer,

    . . then [1] becomes: . (6S + 2D + 1)\cdot\dfrac{639,610}{13} \:=\:192,000,000


    \text{And we have: }\;\underbrace{6S + 2D + 1}_{\text{This is an integer}} \;=\;\dfrac{1,920,000}{\frac{639,610}{13}} \;=\;\underbrace{39.02378012}_{\text{This is not!}}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    Perhaps there is a typo in that answer.

    Maybe it is: .49,230 \frac{10}{13}\:=\:\dfrac{640,\!000}{13}

    Then [1] becomes: . (6S + 2D + 1)\cdot\dfrac{640,\!000}{13} \:=\:1,\!920,\!000


    This gives us: . 6S + 2D + 1 \:=\:39

    . . but why should this be true?
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  3. #3
    Newbie andro45's Avatar
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    OMG! thanks for the reply! that was so great.
    i cannot understand, her book of Puzzles to puzzle you has its 40th edition now, why such a thing should happen to the book of the "HUMAN COMPUTER"?
    i'm confused.

    thanks again to you,
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  4. #4
    MHF Contributor
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    If "least possible" people involved:
    xxmother(1) : 128000
    daughter(1) : 256000
    xxxxsons(2) :1536000
    xxxxtotal(4) : 1920000

    4 people
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  5. #5
    Newbie andro45's Avatar
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    Dear Wilmer, so how do you interpret the given answer:


    thanks
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  6. #6
    MHF Contributor
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    As somebody playing a joke on us!
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