Well, the 3.80/6 EUR fare is just for the rack railway. On top of that, one has to add the 4-zones ticket from Barcelona, and the fare for the use of either or both of the two funiculars (Santa Cova and Sant Joan).
As Catalans have always had business-oriented minds
there are three very interesting combined tickets:
- Combinat: train r/t Barcelona + r/t rack railway for 6.80 EUR
- TransMonserrat: Combinat + r/t BCN Metro ticket + unlimited use of funiculars + entrance to the Audiovisual Area for 21 EUR
- Tot Montserrat: TransMontserrat + entrance to the Museum + lunch at the self-service facility for 34.50 EUR.
Surely there are buses that take you there, but I cannot help on that area.