Ans: $\$540$
Let $\$x$ be the marked price of the fan.
The selling price
$\begin{array}{cl}
= & x \times (1-30\%) \\
= & 0.7x
\end{array}$
Since the profit is $\$78$, then the cost is $\$(0.7x-78)$. Hence, we have
$\begin{array}{rcl}
\dfrac{78}{0.7x -78} \times 100\% & = & 26\% \\
78 & = & 0.182x -20.28 \\
0.182x & = & 98.28 \\
x & = & 540
\end{array}$
Therefore, the marked price of the fan is $\$540$.
