You may also like

problem icon

Burning Down

One night two candles were lit. Can you work out how long each candle was originally?

problem icon

A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

problem icon

Fair Shares?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

Big Fish

Stage: 4 Short Challenge Level: Challenge Level:1

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.