By 8pm all the party guests had arrived. By 9p a third of them had departed . By 10pm a third of those remaining had also departed. By 11pm the same happened again and a third of those remaining had also departed. After this only 8 guests still remained. How many guests arrived?

Suppose total number of guests arrived are x.
At 8 pm, total number guests = x
At 9 pm, total number of guests = $x-\frac{x}{3} = \frac{2x}{3}$
At 10 pm, total number of guests = $\frac{2x}{3}-\frac{2x}{3}\times \frac{1}{3} = \frac{2x}{3}-\frac{2x}{9} = \frac{4x}{9}$
At 11 pm, total number of guests = $\frac{4x}{9}-\frac{4x}{9}\times \frac{1}{3} = \frac{4x}{9}-\frac{4x}{27} = \frac{8x}{27}$
Now according to the question only 8 guests still remained, so we have;
$$\begin{gathered} \frac{8x}{27} = 8 \\ \Rightarrow x = 27 \end{gathered}$$
Therefore total number of guests arrived were 27.