Bought a ticket to Goa, went to Mumbai instead

So Monday morning we went to the train station to buy a ticket to Goa that was departing early in the afternoon. A few hours later we decided we wanted to go to Mumbai instead, so we went back to the station where they told us we could just get the ticket extended once we were on the train by talking to the conductor. (The end of the line was Mumbai.) We also asked around at the station and were repeatedly told when we were on the train, we could just pay the Goa-Mumbai portion of the train ticket..... but that never happened... we told the conductor the first time he came around, but he told us to purchase it later... "later" never happened. From Alleppey to south Goa, where we purchased our ticket to, was about 15 hours, and we reached there early Tuesday morning. We expected someone to check our ticket on Tuesday, but no one ever did. So basically a free 12-hour train ride from south Goa to Mumbai! So, from Alleppey (Alappuzha) to Mumbai we took the Netravathi Express, and rode the train for a total of about 27 hours. Geesh!