Barcelona Arts' investment in Costa del Sol Ltd. should be classified as follows:

Barcelona Arts, owning 10% of Costa del Sol Ltd.'s shares, does not have significant influence over Costa del Sol Ltd. based on the typical 20% threshold. However, Sevilla Inc., which is 55% owned by Barcelona Arts, holds 35% of Costa del Sol Ltd.'s shares. Since Sevilla Inc. is a subsidiary of Barcelona Arts, we need to consider the combined holdings of both Barcelona Arts and Sevilla Inc.

When combining the holdings of both Barcelona Arts and Sevilla Inc., they hold together 45% of Costa del Sol Ltd. This level of ownership, while significant, does not automatically confer control. Control typically requires more than 50% ownership. However, the combined holdings do indicate significant influence.

Therefore, the investment in Costa del Sol Ltd. should be classified as an "associate" by Barcelona Arts. The classification would be:

An associate