# Aunti's Share!

• Aug 25th 2010, 07:07 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}

-----------------------------------
i've asked many ppl, but nobody solved it!
• Aug 25th 2010, 09:23 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 $1,920,000 in this manner: Every son sould receive three times as much as a daughter, and that every daughter should get twice as much as their mother. What is my aunt's share? The answer is: .$\displaystyle 49200\frac{10}{13}$. Impossible! Let$\displaystyle x$= the mother's share. Then$\displaystyle 2x$= each daughter's share. And$\displaystyle 6x$= each son's share. Let$\displaystyle S$= number of sons. . . They will receive$\displaystyle 6Sx$dollars. Let$\displaystyle D$= number of daughters. . . They will receive$\displaystyle 2Dx$dollars. Their mother will receive$\displaystyle x$dollars. Hence: .$\displaystyle 6Sx + 2Dx + x \;=\;1,\!920,\!000$And we have: .$\displaystyle (6S + 2D + 1)x \;=\;1,\!920,\1000$.[1] If$\displaystyle x \:=\:49,200\frac{10}{13} \:=\:\dfrac{639,610}{13}$is the answer, . . then [1] becomes: .$\displaystyle (6S + 2D + 1)\cdot\dfrac{639,610}{13} \:=\:192,000,000 \displaystyle \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!}}$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Perhaps there is a typo in that answer. Maybe it is: .49,230$\displaystyle \frac{10}{13}\:=\:\dfrac{640,\!000}{13}$Then [1] becomes: .$\displaystyle (6S + 2D + 1)\cdot\dfrac{640,\!000}{13} \:=\:1,\!920,\!000 $This gives us: .$\displaystyle 6S + 2D + 1 \:=\:39\$

. . but why should this be true?
• Aug 25th 2010, 09:49 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 25th 2010, 11:54 PM
Wilmer
If "least possible" people involved:
xxmother(1) : 128000
daughter(1) : 256000
xxxxsons(2) :1536000
xxxxtotal(4) : 1920000

4 people
• Aug 26th 2010, 08:43 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, 09:44 PM
Wilmer
As somebody playing a joke on us!