# Thread: Aunti's Share!

1. ## 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:
$49200\frac{10}{13}$

-----------------------------------
can anyone get the answer!!!!?
i've asked many ppl, but nobody solved it!

2. 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 $1,920,000 in this manner: Every son sould receive three times as much as a daughter, and that every daughter should get twice as much as their mother. What is my aunt's share? The answer is: .$\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?

3. 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,

4. If "least possible" people involved:
xxmother(1) : 128000
daughter(1) : 256000
xxxxsons(2) :1536000
xxxxtotal(4) : 1920000

4 people

5. Dear Wilmer, so how do you interpret the given answer:
$49200\frac{10}{13}$

thanks

6. As somebody playing a joke on us!

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### When my unclc in Madura died recently, he left a will, instructing his executors to divide his estate of Rs. 1,920,000 in this manner: Every son should receive three times as much as a daughter, and that every daughter s

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