The sum of ages of Belén and Ana is 60 years old, with Belén lying about her age being 24.
Let's analyze the conversation: Ana is older than Carla. Belén is 24 years old. Carla is 16 years old and double Belén's age. Given that only one person is an adult and one is lying, Belén must be the one lying about her age. If Belén is lying about her age being 24, then Carla cannot be 16. Hence, Carla is the adult. Ana, being 20 years older than Carla, must be 36 years old. Therefore, the sum of Belén and Ana's ages is 36 + 24 = 60 years old.
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