$A$ and $B$ enter into a partnership with capitals in the ratio $3 : 5$. After $6$ months, $C$ joins the business with an amount equal to that of $B$. At the end of $1$ year, in what ratio should the profit be divided among $A$, $B$, and $C$?

Options:

• A: $6 : 10 : 5$
• B: $3 : 5 : 5$
• C: $6 : 5 : 10$
• D: $3 : 10 : 5$

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