Why do the king and the duke add $415 of their own money to the money hidden in the cellar?

The King is worried that if the gold is short, people will think he and the Duke stole it, so to avoid suspicion, they use their own money to make up the difference, planning to swindle even more money from the trusting family later.

Masquerading as the British brothers of the recently deceased Peter Wilkes, the King and the Duke learn that Wilkes has left his brothers $6000 in gold, which is hidden in the cellar. When they fetch the gold and find it short, they replace the money with their own, then, to impress the family by their generosity and gain their unquestioning respect, they give the total amount to the dead man's daughters. As anticipated, the daughters are completely grateful, and later, when the family doctor comes and accuses the two scoundrels of being frauds, Mary Jane, the oldest, demonstrates her total faith in the King and the Duke. She returns the money to them, and instructs them, "Take this six thousand dollars, and invest for me and my sisters any way you want to, and don't give us no receipt for it" (Chapter XXV).