# Aunti's Share!

• Aug 25th 2010, 08:07 PM
andro45
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:
http://www.freemathhelp.com/cgi-bin/...0\frac{10}{13}

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i've asked many ppl, but nobody solved it!
• Aug 25th 2010, 10:23 PM
Soroban
Hello, andro45!

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

Quote:

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?
• Aug 25th 2010, 10:49 PM
andro45
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,
• Aug 26th 2010, 12:54 AM
Wilmer
If "least possible" people involved:
xxmother(1) : 128000
daughter(1) : 256000
xxxxsons(2) :1536000
xxxxtotal(4) : 1920000

4 people
• Aug 26th 2010, 09:43 PM
andro45
Dear Wilmer, so how do you interpret the given answer:
http://www.freemathhelp.com/cgi-bin/...0\frac{10}{13}

thanks
• Aug 26th 2010, 10:44 PM
Wilmer
As somebody playing a joke on us!