Puzzle with twins

Question

Dying someone appointed in the will the following: If his pregnant wife giving birth to a son , then she will inherit 1/3 of the estate and his son 2/3 . If giving birth to daughter , then she would inherit 2/3 of the property and the daughter 1/3 . The woman gave birth to twins after the death of her husband , a boy and a girl .How will be distributed the father's estate?

Any ideas or hints?

Answer 1

The wording here is really bad and ambiguous, but the answer to this puzzle is that if

• the son inherits $4/7$ of the estate,
• the wife inherits $2/7$ of the estate, and
• the daughter inherits $1/7$ of the estate,

the proportions between wife-son ($1:2$) and wife-daughter ($2:1$) will still hold.

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To find these values, translate the problem into equations: we want the wife to have two-thirds of what the wife and daughter share, and one-third of what the wife and son share. Also, the sum of their shares should obviously be $1$, i.e. everything. Altogether we have

$$\begin{cases}w = \frac 23 (w + d) \\ w = \frac 13 (w + s) \\ w+s+d = 1\end{cases} \iff \begin{cases}\frac 12 w = d \\ 2 w = s \\ w+s+d = 1\end{cases}$$

Plugging the 1st and 2nd equations into the third gives us $w + 2w + \frac 12 w = 1$, or $\frac 72 w = 1$, which means $w = \frac 27$. From there we can use the remaining equations to find $s$ and $d$.

Answer 2

Isn't it much simpler to assign a value of 1 to the daughter, 2 to the wife and 4 to son? Adding those values totals to 7. The ratios are then easily derived by placing the assigned values over the total to yield:

1/7, 2/7 and 4/7