Suppose four horses - A,B,C, and D - are entered in a race and the...

Each of the horses has a certain return when they win, A is a $6\times$ return, B is $5\times$, C $4\times$, and D $3\times$. In general say you have a set of horses $H_i$ that each have a return $r_i$, and you bet some total amount $B$ with $B_i$ on each horse $H_i$. As long as $B_i\ge \frac{B}{r_i}$ for all $i$, you will not lose money. That is because one of the $H_i$ will win, and that bet will give you $B_i{r}_i\ge B$, so you end up with at least as much as you started. To maximize your guaranteed winnings, you want to maximize the minimum $B_i{r}_i$, as $B_i{r}_i-B$ is your net profit. This will happen when each $B_i{r}_i$ is equal, which occurs when
$B_i=\frac{\frac{B}{r_i}}{\sum \frac{1}{r_i}}$
and your guaranteed profit is
$\frac{B}{\sum \frac{1}{r_i}}-B$
This is why in a real horse race $\sum \frac{1}{r_i}$ will always be greater than $1$(if for some reason it's not go make a big bet!). In this question it was only $.95$ allowing you to make a nice little profit!