If there are f females and m males then $86=8f+9m=8(f+m)+m$. Now $86=8\times 10+6=8 \times 9+14...$ Only the first of these is feasible so m=6 and f=4. Therefore the ratio of male to female fish is $3:2$.

Alternatively, dividing the stripes into groups of $8$, there are $6$ left over. One left over is produced by each male, so there are $6$ or $14$ or... males. However, as $14 \times 9 = 126 > 86$, there must be six males. Then, this leaves $32$ stripes remaining, so there are $4$ females. Therefore the ratio of male to female fish is $3:2$.

*This problem is taken from the UKMT Mathematical Challenges.**View the archive of all weekly problems grouped by curriculum topic*

View the current weekly problem