Copyright © University of Cambridge. All rights reserved.

'Big Fish' printed from https://nrich.maths.org/

Show menu


Answer: $54$ kg


Body weighs $b$ kg, head $h$ kg, tail $9$ kg

  $h=9+\frac13b$ and $b=h+9$, so $$\begin{align}b&=h+9\\
&=\left(9+\tfrac13b\right)+9\\
&=\tfrac13b+18\\
\Rightarrow\tfrac23b&=18\\
\Rightarrow\ \ b&=27\end{align}$$
So $h=9+\frac13\times27=18$ and the fish weighs $27+18+9=54$ kg


This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.