In a club of $300$ members, $160$ like swimming, $140$ like cycling and $60$ like both. What fraction of the total members like exactly one activity?

Given:
Total members ($N$) = $300$
Members who like swimming ($S$) = $160$
Members who like cycling ($C$) = $140$
Members who like both ($S\cap C$) = $60$

Let's find the number of members who like exactly one activity:

* Members who like swimming only = $S-(S\cap C)=160-60=100$
* Members who like cycling only = $C-(S\cap C)=140-60=80$

Total members who like exactly one activity = $100+80=180$.

The required fraction of total members is:

$$\text{Fraction}=\frac{180}{300}=\frac{18}{30}=\frac{3}{5}$$