It is actually the typos I made and corrected right after u made your post. ( Besides that it is a homework, I am frustrated for not solving this even after spending 2 days google around )
I will start the beginning by myself.
Before titration started:
Na₂CO₃ + 2 HCl -> 2NaCl + H₂O + CO₂
NaOH + HCl -> NaCl + H₂O
If Barium Chloride is added....
I know that : Na₂CO₃ + BaCl₂ -> NaCl + BaCO₃
But will ? : BaCl₂ + NaOH -> Ba(OH)₂ + 2NaCl
Ba(OH)₂ + CO₂ -> BaCO₃ + H₂O
Volume of NaOH affected??!?!
What do you know about barium and calcium carbonates solubility?
Barium carbonate is insoluble.