54kg

Let the weights in kilograms of the head and body of the fish be $h$ and $b$ respectively. Then $h = 9 + \frac{1}{3} b$ and $b = h+9$. So $b = 9 + \frac{1}{3} b + 9$, that is, $\frac{2}{3} b = 18$, which gives $b = 27$. Hence $h = 18$, so the whole fish weighed 54kg.

*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