1. The denominator of a reduced fraction is 30, find the sum of all such positive rational numbers less than 10.

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1. Xiao Guang 10 points: If a fraction can be simplified to the form $\frac{30 n+r}{30}$, where $n$ and $r$ are integers satisfying $0 \leqslant n \leqslant 9$ and $0 \leqslant r<30$.

When and only when $r$ is coprime with 30, $\frac{30 n+r}{30}$ is a simplified fraction, thus, $r \in\{1,7,11,13,17,19,23,29\}$.

Since $n$ has 10 possible values and $r$ has 8 possible values, and each value of $\frac{30 n+r}{30}$ is unique, the total number of such fractions is $8 \times 10=80$. $\because \quad 10-\frac{k}{30}=\frac{300-k}{30}$,
$\therefore$ the fractions $\frac{k}{30}$ can be paired for calculation.
Thus, the sum of all such fractions is
$$
\begin{array}{c}
\left(\frac{1}{30}+\frac{300-1}{30}\right)+\left(\frac{7}{30}+\frac{300-7}{30}\right)+ \\
\cdots+\left(\frac{149}{30}+\frac{300-149}{30}\right)=40 \times 10=400
\end{array}
$$